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Jorge Pullin: Okay, sorry speaker to this much your subscale who will speak about Korean at the center space times that admit non singular horizons.
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Warsaw LQG: Okay. Hello and welcome.
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Warsaw LQG: So this is actually a joint work of mine with Priscilla on those key that we're doing here and the faculty of physics at the University for so and
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Warsaw LQG: What I want to talk today about at the first the Colonel's and the disk space times they are not the most commonly and contact space dance one considers in GR so to me.
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Warsaw LQG: Until I break down some of their properties.
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Warsaw LQG: Then
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Warsaw LQG: I will introduce the conditions.
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Warsaw LQG: Conditions for the removal of the singularity of the clinical singularity of the horizons in the cabinet and the space times
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Warsaw LQG: Some discussion about what are those singularities.
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Warsaw LQG: And
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Warsaw LQG: What is quite surprising result in the same conditions for the removing of singularity and the singularity, the horizon can be extended to the neighborhoods.
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Warsaw LQG: Of the non singular horizon. So that will be the next point I will talk about. And finally,
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Warsaw LQG: Our work is connected
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Warsaw LQG: To another topic. Our team is working on so connected to the type the horizons on the non trivial fiber abundance of our sphere, and I will show some connection of our long singular horizon to this work.
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Warsaw LQG: As well as some generalization of our results extending to the accelerator cannot see the space times
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Warsaw LQG: In this case, even, can I think the Secret Space Time accelerated, of course.
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Warsaw LQG: So what are the seeds are planted the seed stage names.
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Warsaw LQG: There are solutions to the vacuum Einstein equations with cosmological constant. And it's a four dimensional family parameter is by
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Warsaw LQG: For real numbers, usually, usually interpreted as the muscle my call as the curl parameter connected to the angular momentum of the black hole.
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Warsaw LQG: Just like home is on the cosmological constant background.
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Warsaw LQG: For the sign is
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Warsaw LQG: A sprig can be positive, negative, and there's this one quite exotic parameter called and they're not parameter first discovered in the top not
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Warsaw LQG: Space, which was the extension of fortunes swatches.
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Warsaw LQG: Black Hole.
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Warsaw LQG: And introduction and is not parameter means for us.
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Warsaw LQG: Some, some new to political
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Warsaw LQG: Considerations has to be taken into account.
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Warsaw LQG: So,
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Warsaw LQG: Before I begin, I want to talk about some motivation for our work.
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Warsaw LQG: So,
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Warsaw LQG: The person wanted to investigate just the
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Warsaw LQG: The horizons of the current not the Sitter space times
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Warsaw LQG: Because you know 13 there was there was some results concerning the solutions to the pit of the equations, which provides us with the geometry of the isolated horizons of time thing.
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Warsaw LQG: Any particular one recent ones and paper by the mosquito cleverness garage discusses the family of type the horizons of the topology bundle.
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Warsaw LQG: Which
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Warsaw LQG: When you, when you pose the vacuum is the equations and provided by industry that I selected horizon solutions.
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Warsaw LQG: And those solutions are actually privatized by four parameters so
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Warsaw LQG: We conjecture that probably those horizons should be some relation to the current not until they see their space times because the as well and four dimensional family.
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Warsaw LQG: But as we discovered later this, the decision was
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Warsaw LQG: Quite less obvious than we expected.
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Warsaw LQG: So I'm expecting some results only on the sub family of Colonel
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Warsaw LQG: colonel colonel this space, things are on the family.
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Warsaw LQG: Of the four dimensional family of time the horizons.
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Warsaw LQG: So this is the general form of the
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Warsaw LQG: Current not under the sitter metric and
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Warsaw LQG: There are some
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Warsaw LQG: Some things, one should maybe understand just by looking at this metric. So first thing that
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Warsaw LQG: It can be seen. That's just a generalization of the previously known like how solutions. So for the for the not parameter equals zero, we will cover the
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Warsaw LQG: I think this either spacetime.
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Warsaw LQG: And for
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Warsaw LQG: A equal to zero and lambda equal to zero. So we actually covered the original thousand ounce metric
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Warsaw LQG: So there are a couple of
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Warsaw LQG: Things that are quite suspicious. Like, for example,
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Warsaw LQG: There are places in the world where we divide in that component, the component of metric so
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Warsaw LQG: And my assumption the function P which appears in the beta coefficient has to be has to be positive. It also guarantees us that the
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Warsaw LQG: Them signature is Lawrence young so we use, minus, plus, plus, plus.
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Warsaw LQG: On the other hand, we also divided by the function kill and dysfunction, kill, as we said later so is corresponding to the
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Warsaw LQG: To the kidney crisis on the cabinet.
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Warsaw LQG: Space times
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Warsaw LQG: Yes. And what's also important about this metric that
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Warsaw LQG: As all of the Type D solutions we have algebra have any factors spammed by to committing deals. So we have
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Warsaw LQG: The opportunity which is time translation symmetry.
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Warsaw LQG: And also the over the five, which means for us that this metric is as a rotational symmetry.
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Warsaw LQG: Yes, so
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Warsaw LQG: They want to discuss the clinical singularity.
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Warsaw LQG: Which stems from the fact that when we, when you consider this one form a defy which appeared
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Warsaw LQG: Appeared in the time like metric component
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Warsaw LQG: They discovered that
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Warsaw LQG: If the L is not zero. So when we have some not parameter
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Warsaw LQG: This one phone does not doesn't punish at the pole data equals the pie. So this means for us that the G is not continuous, and the whole semi access Sita equal to buy
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Warsaw LQG: And obviously this is a coordinate and dependent statement. So one could choose another coordinate and accordingly transform this singular access. So for example, if you introduce
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Warsaw LQG: The prime which is T minus four L fi then
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Warsaw LQG: Our one phone transfers and
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Warsaw LQG: Such that
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Warsaw LQG: It then becomes a prime the data and then
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Warsaw LQG: And discussing squared is for us that
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Warsaw LQG: This one doesn't management and the semi access data at 1.0 and the genius not continues and
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Warsaw LQG: At the at the other similar axes of course for any other choice of the of the team coordinators, for example, and TVs equals t minus two, five should be to find
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Warsaw LQG: This one from doesn't punch that the balls balls and the jury is not continuous. In the whole access so
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Warsaw LQG: One of our refers to this space times as having the gravitational magnetic monopole while
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Warsaw LQG: When this singular axes corresponds to the
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Warsaw LQG: To the Mr string connecting the magnetic the bone and as was in that case, we could
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Warsaw LQG: Talk about the gravitational magnetic monopole one could choose engage such thoughts, want to switch which access is singular.
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Warsaw LQG: And
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Warsaw LQG: For the generic values of parameters. So of the mass exposure constant current not parameters the space time you singular in at least one poll
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Warsaw LQG: And usually, usually above us.
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Warsaw LQG: So there was some propositions in how to remediate those problems.
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Warsaw LQG: For example, for example.
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Warsaw LQG: Mr considered
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Warsaw LQG: Originally I thought not space. So a limit of without care parameter AND CHRIS MITCHELL constant
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Warsaw LQG: When we could take
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Warsaw LQG: Don't know senior solutions. So one with the singular axis at the southern hemisphere and one and the
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Warsaw LQG: Senior axis and the Northern Hemisphere and then we take from the, from the left one. The know them not singular hemisphere and glue it to the
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Warsaw LQG: Southern
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Warsaw LQG: Of the right
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Warsaw LQG: Space and
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Warsaw LQG: In this way we arrived at the
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Warsaw LQG: At the top, not space time which is which is not senior
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Warsaw LQG: At the slides, the slides cost of having a periodic to coordinate
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Warsaw LQG: And then the resulting topology is a free spirit times, times around this topic, not space. So our results.
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Warsaw LQG: And remained results states that this is not enough.
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Warsaw LQG: In the general case in the generic case of digital space times so
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Warsaw LQG: One can one can make is doing in the arbitrary case. But then one discovers that
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Warsaw LQG: We don't have this
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Warsaw LQG: Resulting topology of US frame and our glowing is such that the horizon that the holes are still not differentiable
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Warsaw LQG: So what we discovered
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Warsaw LQG: Is that the glowing is differentiable
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Warsaw LQG: And in fact we by investigation explicitly check that at least twice differentiable, only if this is condition is satisfied. So if we overlap that was to a squared r squared plus two r zero squared.
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Warsaw LQG: Where r zero is a radius of
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Warsaw LQG: Have a
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Warsaw LQG: Clinic Christ on which we want to make non singular
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Warsaw LQG: So a couple, a couple of words about the current the sitter horizons.
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Warsaw LQG: So, as I told you before the horizons are
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Warsaw LQG: Correspond to the to the zeros of this Q function.
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Warsaw LQG: Actually just a polynomial polynomial in in the coordinates are so it's for for the recording recording phenomenal so
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Warsaw LQG: We have up to four killing horizons and one can check that.
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Warsaw LQG: In fact surfaces of our he was to our CEO and our surface surfaces and they are crayons and their clinic horizons never buy this Kinney vector side which we use extensively in this
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Warsaw LQG: In our research paper.
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Warsaw LQG: Which is just a just a certain linear combination of the two factors that we
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Warsaw LQG: That we have. And maybe one important thing to notice.
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Warsaw LQG: Is that
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Warsaw LQG: Is that
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Warsaw LQG: This
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Warsaw LQG: Killing vector field.
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Warsaw LQG: Explicitly depends on the right is on the horizon.
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Yes.
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Warsaw LQG: So,
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Warsaw LQG: Actually, the, the original metric and the original form the metric that I showed
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Warsaw LQG: Was singular at the at the horizon. So, one cannot use it to describe the
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Warsaw LQG: The Christ and geometry. But what we can do is we can introduce the slightly change call frame. So this coordinate be is an analog over
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Warsaw LQG: Of an advanced time
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Warsaw LQG: And actually, it just reduces to the advanced time for
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Warsaw LQG: For the suitcase.
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Warsaw LQG: And also to introduce some some twisted and twisted ankle coordinate
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Warsaw LQG: Which is not, not necessarily in the into taking cases we have here and a
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Warsaw LQG: And then
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Warsaw LQG: You can you can calculate the there's nothing metric that is announcing that are at the horizon. So as you can see
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Warsaw LQG: This this troublesome.
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Warsaw LQG: Factor of one overkill, which was connected to them the r squared coordinate is no longer appears so our, our metric is is totally fine. And the horizon.
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Warsaw LQG: And here we explicitly say that the surfaces.
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Warsaw LQG: Of
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Warsaw LQG: Constant. Constant. Constant radius.
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Warsaw LQG: R zero
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Warsaw LQG: Gives us the agenda metric
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Warsaw LQG: On the horizon.
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Warsaw LQG: And those sigma zero functions and roles, your functions are just the previous functions introduced
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Warsaw LQG: With the metric components.
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Warsaw LQG: But for the horizon.
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Warsaw LQG: Ranges.
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Warsaw LQG: So we want to want to introduce
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Warsaw LQG: You coordinates on this singular horizon.
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Warsaw LQG: And
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Warsaw LQG: In fact, this coordinates expo and x ray are the coordinates on the space of now generators of the horizon.
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Warsaw LQG: And
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Warsaw LQG: When completed with this coordinate style those coordinates.
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Warsaw LQG: We just need coordinate systems on the on the horizon and
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Warsaw LQG: Great vibe from this curtness
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Warsaw LQG: That they are somewhat perpendicular to the
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Warsaw LQG: Today, killing better
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Warsaw LQG: So, so the size of X to an extra
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Warsaw LQG: Damage
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Warsaw LQG: So make a particular choice.
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Warsaw LQG: Of the talk. Responding to
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Warsaw LQG: To be and
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Warsaw LQG: X to tune the data and expect to some some combination of the and
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Warsaw LQG: And fight to the connected with
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Warsaw LQG: Collectors also to this Amiga which define the
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Warsaw LQG: The killing machine vector
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Warsaw LQG: And then we have this
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Warsaw LQG: This new
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Warsaw LQG: Horizon metric in this new ordinance when what it is even. It's even easier to see that he said that Jeanette degenerate metric on them on the horizon.
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Warsaw LQG: And one thing I should also point out is that
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Warsaw LQG: Will probably use this fact that
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Warsaw LQG: In this in this coordinate the tower is just side.
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Warsaw LQG: So it will simplify some some notation.
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Warsaw LQG: Yes, and
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Warsaw LQG: Maybe some intuitions about once or this clinical singularity.
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Warsaw LQG: And responsible, so we can we can consider section of their horizon and in many cases, one one expect this section of the horizon to have the topology of the spear.
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Warsaw LQG: But there might be some some problems in the Pops.
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Warsaw LQG: In fact, our, our previous metric
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Warsaw LQG: Was analytic everywhere.
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Warsaw LQG: Except for me from the, from the post. So, so what I want to survey to study this metric. The only suspicious points are
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FAU Erlangen: Me. Can I make a comment is, so actually this figure, which is the next slide. It is the it's not a slice of the horizon. It is the projected space. This is the space of the knowledge generators and this is exactly this metric from the previous slide.
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Warsaw LQG: Yes, yes.
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Warsaw LQG: So what can go wrong in the polls, is that we, we can have some kind of some kind of wedge this this web this
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Warsaw LQG: Corresponds to this clinical singularity. And one way of saying it is
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Warsaw LQG: Is that we simply chose chose the range of the angular Coordinates. Coordinates wrong.
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Warsaw LQG: And
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Warsaw LQG: I would like their methods is based on considering and such loops.
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Warsaw LQG: Around
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Warsaw LQG: Circles circles around the symmetry access and in the case of the
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Warsaw LQG: Way from far from the pole, this, this ratio should obviously be to buy, but there might be some problems in the post. And then we'd like to impose the conditions.
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Warsaw LQG: That duration of circumference to the radius in the post will also be
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Warsaw LQG: Like on the to secure. So to buy
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Warsaw LQG: Yeah, so that's exactly. That's exactly what I'm going to talk now. So, so far we haven't made many assumptions about the the nature of the coordinates x to an extreme. And in fact,
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Warsaw LQG: In fact, we didn't assume that there are spiritual coordinates.
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Warsaw LQG: So explain
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Warsaw LQG: Expands
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Warsaw LQG: expands on some interval close at the one side, which is two pi time. See, and later on finding this the suitable see constant will allow us to remove that
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Warsaw LQG: The single the
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Warsaw LQG: Clinical singularity.
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Warsaw LQG: So,
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Warsaw LQG: So actually made a little bit of assumptions that, but there may be not assumptions, because they can be seen from the, from the form of the metric that x to y equals zero corresponds to the single bond and
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Warsaw LQG: So our poll is a single point, and I still equals to some other concerns our circles on this.
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Warsaw LQG: Space of no generators
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Warsaw LQG: Now we have to define
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Warsaw LQG: Went to consider the circles of a constant stone and define for them.
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Warsaw LQG: There's a conference which is an integral of the
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Warsaw LQG: Of the of the components.
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Warsaw LQG: And thank you, free free
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Warsaw LQG: Along the circle and then we want to introduce the radius which we calculate in such a in different ways in different calls different polls and this choice is made so that
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Warsaw LQG: So that the radius calculated along this
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Warsaw LQG: And this
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Warsaw LQG: Money for that. You want some beautiful
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Warsaw LQG: Spirit is calculated along along just disappear and
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Warsaw LQG: The radius on the northern
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Warsaw LQG: Hemisphere.
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Warsaw LQG: should train to zero as we approach the pole and the same goes for the rate is defined the southern hemisphere. So it should also shrink to zero when we approach approach the boss.
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Warsaw LQG: So as I mentioned earlier, our condition.
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Warsaw LQG: Our condition that the radius that the ratio of the circumference to the radius.
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Warsaw LQG: Has to be checked in, in the suspicious points of our metrics on the pose and they simply corresponds to taking the limits of the circumference and their ideas.
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Warsaw LQG: In boats boats and
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Warsaw LQG: Making strength of this limit has to be to buy so that we will cover the result from a sphere.
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Warsaw LQG: And so because in the in the integration.
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Warsaw LQG: Interval appears. This is Kelly constancy. And he says, he says the the condition on this is getting constant. So for the. So the first thing is that we want.
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Warsaw LQG: That we want this rescaling constant to be to be the same in both balls, so that's that's what this first equations equations stems from and then we see that there's Kelly constantly simply one over the, over zero so that we have to fight for example in in this in this Poland.
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Warsaw LQG: If this part satisfies
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Warsaw LQG: The first constraint and we also had
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Warsaw LQG: To to find and the brief reminder about dysfunction be so in general this condition this condition.
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Warsaw LQG: Should depends on the on all of the parameters of the Colonel's and the Sitter space time. So we have
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Warsaw LQG: Except from like from them. So
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Warsaw LQG: So we have great news. Not parameter
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Warsaw LQG: Awesome. Sure appears because mariska constant
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Warsaw LQG: So in five our, our constraint is quite with the study because we will cover the previously known.
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Warsaw LQG: This no solutions which are which do admit Monsignor our horizons. So first, if one says, because much constant to zero then then be PLC one piece of pie are equal. And then the only choice to make this distraction. One is to
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Warsaw LQG: Either have l equal to zero and so that the squad takes care of the miners or have a equal to zero. And those corresponds to either current or 12 not
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Warsaw LQG: Space times
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Warsaw LQG: Similarly,
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Warsaw LQG: Similarly, if one
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Warsaw LQG: Takes equal to zero.
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Warsaw LQG: So some curve and visitors FaceTime or
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Warsaw LQG: Equal to zero and some some London so told not to disturb space time. Then we also have
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Warsaw LQG: Feels very well be of bison, so it's good that our, our constraint recovers the non non singular solutions.
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Warsaw LQG: But there's one more choice. One more solution to this equation.
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Warsaw LQG: And this distortion requires a couple of assumptions. So it requires that all of the
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Warsaw LQG: All of the parameters are non zero so
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Warsaw LQG: So, so, in particular, we cannot have any symptoms are
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Warsaw LQG: Not solution without customers are constant
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Warsaw LQG: And this is this is the constraint. I was, I was thinking earlier and it might be also
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Warsaw LQG: Intuitive to see why why it doesn't admit zero because Mitchell, a constant because we we actually, when do I mean the rescaling constant, we, we did. Bye bye. Bye.
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Warsaw LQG: Then our, our constraints has are zero and we like to probably would rather
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Warsaw LQG: Maybe not in general the the space time is prioritized by Master
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Warsaw LQG: actually solving solving
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Warsaw LQG: We can solve and the queue of our zero equals zero and get and get the, the mass of the black hole.
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Warsaw LQG: So a couple of remarks about the geometry of the space of the now geneticists decry some
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Warsaw LQG: Some now.
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Warsaw LQG: Now the coordinates.
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Warsaw LQG: X two X extreme
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Warsaw LQG: Has this range, when we determined determined the rescaling constant is one over P of zero and one could really nicely.
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Warsaw LQG: describe those those horizons, because we can explicitly calculate the value of the other area so
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Warsaw LQG: It's somewhat connected to the reason why we cannot have a negative customer Chad constant
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Warsaw LQG: Because as long can see then the area would be negative. And in fact, the this condition for lambda
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Warsaw LQG: Complaints only, only some positive numbers and then the squares of the parameters. So, so we have no no singular bicker not emptying the Sitter space times with
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Warsaw LQG: With customers with negative because much a constant.
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Warsaw LQG: So,
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Warsaw LQG: We explicitly check that. Our philosophy is at least twice differentiable at the polls. So, so that the metric that the components of the metric or at least twice in different ways differentiable
266
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Warsaw LQG: But contrary to the for example current horizons.
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Warsaw LQG: They do not have
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Warsaw LQG: The topology over to spear times, times our. So actually, our horizons have some of the apology have some non trivial.
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Warsaw LQG: Fiber been over a stone, such as such as, for example, hope bundle.
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Warsaw LQG: And there is also some
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Warsaw LQG: Some tricky results, some tricky.
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Warsaw LQG: parts of ourselves, is that
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Warsaw LQG: This condition explicitly depends on the on the radius of the horizon.
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Warsaw LQG: So,
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Warsaw LQG: In general, if we if we have one
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Warsaw LQG: Singular horizon.
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Warsaw LQG: Then we could ask, what about the up to free other horizons. And in fact, this, this, this condition tells us
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Warsaw LQG: That if you make one of the crisis one singular, then there's no no possibility of making other horizons non singular
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Warsaw LQG: Yes, so the next. The next thing we consider was where the the neighborhood of the horizons and
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Warsaw LQG: To do that we introduced the space of the orbits the orbits of the Kinect oxide and directly the horizon.
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Warsaw LQG: And to do that we chose
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Warsaw LQG: Chose the coordinates, such as exciting equals to some detail. And in fact, the
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Warsaw LQG: If the code is that I'll show you in a minute quite similar to those for the horizon.
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Warsaw LQG: And then if we if you can write the metric in this
285
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Warsaw LQG: New Horizons in this form.
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Warsaw LQG: Then
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Warsaw LQG: Then there are a couple of nice nice things about about this way of writing the metric. So for example, this Q part so que que ha the X the X the X j correspond to the metric on the space of the orbits of the better side. So one could maybe better understand what this metric is
288
00:34:03,060 --> 00:34:07,650
Warsaw LQG: Is if we consider that the the space time
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Warsaw LQG: Is
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Warsaw LQG: Created by the by the flows on the kinetic side and
291
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Warsaw LQG: Each
292
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Warsaw LQG: And this low corresponds to
293
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Warsaw LQG: The clinic observers and then
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Warsaw LQG: Then the skill measure space time distance between between some neighboring kingdoms observers.
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Warsaw LQG: Along alongside
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Warsaw LQG: So some other some other part is
297
00:34:42,840 --> 00:34:46,170
Warsaw LQG: This one from ditto plus and the dog is
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Warsaw LQG: Divided by Jane Doe.
299
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Warsaw LQG: The x
300
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Warsaw LQG: Which is
301
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Warsaw LQG: Which we call the rotation connection one form.
302
00:34:58,140 --> 00:35:06,660
Warsaw LQG: Because it is somehow connected to the to the rotation of the space and also this one firms actually a connection on the
303
00:35:08,130 --> 00:35:11,970
Warsaw LQG: Connection form on the hub bundle which
304
00:35:14,160 --> 00:35:16,380
Warsaw LQG: Of which the our horizon structure.
305
00:35:17,790 --> 00:35:18,750
Warsaw LQG: So,
306
00:35:20,310 --> 00:35:24,600
Warsaw LQG: What's the benefit of writing that the metric in this way. So all of these
307
00:35:25,920 --> 00:35:31,950
Warsaw LQG: All of these objects that they described as well that loves function they have they have
308
00:35:33,600 --> 00:35:45,300
Warsaw LQG: Geometric geometric meaning besides some some coordinated expression. So it's, it's actually good because our considerations about the horizon. We're also
309
00:35:46,650 --> 00:35:56,250
Warsaw LQG: Kind of geometry, because the horizon is a it's an object which is defined geometry geometry and not not in some particular coordinates.
310
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Warsaw LQG: And so this is this is the analytical approach.
311
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Warsaw LQG: In the neighborhood of that the crisis.
312
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Warsaw LQG: Some will we make some particular choice of the of the coordinates.
313
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Warsaw LQG: And this choice is quite similar to the
314
00:36:19,830 --> 00:36:25,380
Warsaw LQG: To the choice for the horizon. So, and before we had Tao equal to some
315
00:36:27,330 --> 00:36:37,200
Warsaw LQG: Advanced code and advice advanced and coordinate. Now we have simply simply team and also there is x one, which is just the radius.
316
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Warsaw LQG: And the rest is is the same as in the horizon case.
317
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Warsaw LQG: And then we can ride the, the original American in this new form.
318
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Warsaw LQG: For me, which we
319
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Warsaw LQG: Extract
320
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Warsaw LQG: The form of the metric on the space of the orbits.
321
00:37:10,440 --> 00:37:23,400
Warsaw LQG: So if you want this this metric to measure distance. Distance between the kink observers, we have to make sure that that we are somehow using the frame which is tangent to the
322
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Warsaw LQG: To the, to the side. So we are introducing introducing new frame this hearted frame.
323
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Warsaw LQG: That exactly satisfies satisfies our property.
324
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Warsaw LQG: Property that is it's it's perpendicular to
325
00:37:45,000 --> 00:37:46,560
Warsaw LQG: The side and
326
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Warsaw LQG: When I say live and this this metric. Q.
327
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Warsaw LQG: On the space of the of the orbits.
328
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Warsaw LQG: And obviously, it has some properties that I would like to discuss now. So first of first of which is the
329
00:38:12,000 --> 00:38:13,500
Warsaw LQG: The signature.
330
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Warsaw LQG: So these components Q human lung.
331
00:38:20,340 --> 00:38:30,630
Warsaw LQG: Close to the horizon, just the non extra mile for aizen which might be some which actually makes a difference here. What kind of Horizon, we do consider
332
00:38:31,470 --> 00:38:47,040
Warsaw LQG: Which wasn't the case, the horizon case on the the previous metric was in qualifying for the for the external horizons or so when when the R zero was a multiple of the function Q
333
00:38:49,230 --> 00:38:52,290
Warsaw LQG: Now we only consider the unknown extreme cases.
334
00:38:54,360 --> 00:39:05,640
Warsaw LQG: So close to the horizon, the cumin. One is proportional to minus g psych side. So when the time is is time like
335
00:39:07,500 --> 00:39:13,380
Warsaw LQG: This component is positive and the other way around. When is space like
336
00:39:14,610 --> 00:39:19,950
Warsaw LQG: To to to buy the assumption that the P is positive. You see, it's also positive everywhere.
337
00:39:21,960 --> 00:39:23,190
Warsaw LQG: And the component
338
00:39:24,270 --> 00:39:24,870
Warsaw LQG: To
339
00:39:26,970 --> 00:39:31,170
Warsaw LQG: The component, feel free. Three also requires us that we are
340
00:39:32,610 --> 00:39:36,900
Warsaw LQG: Supposedly, but only one we are close to the non extra mile horizon.
341
00:39:38,850 --> 00:39:42,420
Warsaw LQG: So this can probably be better seen from from this
342
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Warsaw LQG: Explicit
343
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Warsaw LQG: Form well
344
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Warsaw LQG: Then what we what we did here was just divide by my dysfunction kill and if
345
00:40:01,890 --> 00:40:04,620
Warsaw LQG: In the denominator, the negative part
346
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Warsaw LQG: If it vanishes. Then, then this be science squared 00 squared sigma divided by sigma squared, it's positive. So then we would have
347
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Warsaw LQG: We would have
348
00:40:21,660 --> 00:40:23,250
Warsaw LQG: You feel free positive
349
00:40:24,570 --> 00:40:27,210
Warsaw LQG: And when we consider this this denominator
350
00:40:30,570 --> 00:40:34,560
Warsaw LQG: It goes to zero when we approach the horizon, only if the
351
00:40:35,640 --> 00:40:36,120
Warsaw LQG: If the
352
00:40:37,200 --> 00:40:37,920
Warsaw LQG: R zero
353
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Warsaw LQG: Corresponds to the non singular person.
354
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Warsaw LQG: Otherwise this this second second part. And denominator approaches some concept on even can
355
00:40:52,560 --> 00:40:53,250
Warsaw LQG: Even can
356
00:40:54,450 --> 00:40:56,520
Warsaw LQG: Blow up and this is this is a result
357
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Warsaw LQG: This stems from the fact that the
358
00:41:02,940 --> 00:41:05,640
Warsaw LQG: The metric and and the the space of the
359
00:41:07,620 --> 00:41:13,020
Warsaw LQG: Of the purpose of the killing horizon as well as you find on the way.
360
00:41:15,360 --> 00:41:16,920
Warsaw LQG: If you are far from the horizon.
361
00:41:22,980 --> 00:41:37,770
Warsaw LQG: And this is also some some it's mirrored in the fact that the denominator of the component queue for free. It's actually proportional proportional to the to the length of the
362
00:41:40,560 --> 00:41:41,730
Warsaw LQG: Of the vector side.
363
00:41:42,900 --> 00:41:43,650
Warsaw LQG: So,
364
00:41:45,600 --> 00:41:50,790
Warsaw LQG: If we are close to the to the extra mile for eyes on this component
365
00:41:51,810 --> 00:41:54,120
Warsaw LQG: Feel free. Free to approach the
366
00:41:55,230 --> 00:42:01,200
Warsaw LQG: The component cube for free from the metric on the on the horizon and
367
00:42:03,690 --> 00:42:10,770
Warsaw LQG: That would be fine for us. We have just some extension of the geometry from the horizon to the neighborhood, but
368
00:42:13,410 --> 00:42:18,210
Warsaw LQG: There, there might be some services which are not killing horizons.
369
00:42:21,330 --> 00:42:21,780
Warsaw LQG: And
370
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Warsaw LQG: All the way to the the norm on tech side also vanishes. So that's kind of a natural range of the applicability of our of our metals.
371
00:42:40,350 --> 00:42:48,060
Warsaw LQG: Yes, so. So, the important part here is that that this metric tends to the present metric. If the R zero is a single
372
00:42:49,260 --> 00:42:53,040
Warsaw LQG: Singular it corresponding to the non western horizon.
373
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Warsaw LQG: So the considerations from the previous slide, it has to the conclusion that
374
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Warsaw LQG: First, we, we should consider here on the, the non external four zones.
375
00:43:08,700 --> 00:43:22,260
Warsaw LQG: So are in order to to assure that our signature is either plus, plus, plus or minus plus plus one. What's really important for us is that, and that
376
00:43:23,700 --> 00:43:25,380
Warsaw LQG: There are two classes at the end here.
377
00:43:27,330 --> 00:43:28,080
Warsaw LQG: And also,
378
00:43:29,370 --> 00:43:34,950
Warsaw LQG: There are a couple of statements that dependent on the fact that we are close to the horizon. So in fact,
379
00:43:35,970 --> 00:43:36,690
Warsaw LQG: Our metric
380
00:43:38,130 --> 00:43:44,670
Warsaw LQG: Or a metric is defined on the on some on some future or past neighborhood on the horizon.
381
00:43:47,250 --> 00:43:47,790
Warsaw LQG: And this
382
00:43:49,470 --> 00:43:50,580
Warsaw LQG: Is a short assures us that
383
00:43:51,990 --> 00:43:54,120
Warsaw LQG: That excite does not doesn't vanish.
384
00:43:55,470 --> 00:43:55,950
Warsaw LQG: And
385
00:43:57,360 --> 00:44:00,660
Warsaw LQG: And this component to free free is well defined.
386
00:44:06,060 --> 00:44:06,660
Warsaw LQG: So,
387
00:44:08,250 --> 00:44:09,480
Warsaw LQG: Again, we want to
388
00:44:11,310 --> 00:44:12,600
Warsaw LQG: We want to consider.
389
00:44:17,250 --> 00:44:28,770
Warsaw LQG: Want to consider whether this metric is is analytic and of course it should be analytic everywhere was defined, apart from the posts on the same case as the horizon.
390
00:44:30,240 --> 00:44:32,310
Warsaw LQG: And then the only the only
391
00:44:35,670 --> 00:44:44,340
Warsaw LQG: The only part of this metric, which can be which can be singled out the post have some problems is the pullback of this metric to to the surfaces.
392
00:44:45,570 --> 00:44:56,580
Warsaw LQG: With the surfaces of X one constant but not equal to the horizon radios will, which was the case that when considered earlier.
393
00:45:01,980 --> 00:45:04,500
Warsaw LQG: For this for this two dimensional matrix.
394
00:45:06,120 --> 00:45:10,890
Warsaw LQG: We can look in again use the framework of considering loops.
395
00:45:11,940 --> 00:45:12,780
Warsaw LQG: loops around
396
00:45:14,610 --> 00:45:15,870
Warsaw LQG: The rotational axis.
397
00:45:17,880 --> 00:45:26,580
Warsaw LQG: So the, the circumference of the circle and the radius are defined just just in the same way as for the horizon.
398
00:45:31,440 --> 00:45:42,030
Warsaw LQG: And what we somewhat surprisingly discovered is that when we apply this framework of of loops and we impose this condition that
399
00:45:42,540 --> 00:45:58,050
Warsaw LQG: And that the ratio of circumference to the radius should be two pi in the post that we recover exactly the same condition is for the horizon, so that P zero equals to some friction and then p of by
400
00:45:59,580 --> 00:46:00,120
Warsaw LQG: And
401
00:46:01,980 --> 00:46:06,600
Warsaw LQG: So what it means is that if we can some some
402
00:46:07,770 --> 00:46:16,110
Warsaw LQG: Parameters that I've made no single our horizon, then at the same time simultaneously those parameters.
403
00:46:16,920 --> 00:46:30,420
Warsaw LQG: Remove the singularity from the, from the future or past neighborhood of the horizon. And what's also important to stress here is that the our rescaling constant is still simply one over
404
00:46:31,710 --> 00:46:40,980
Warsaw LQG: You know, and the function PR zero does not depend on the value on the coordinate or here on the x coordinate, so
405
00:46:44,880 --> 00:46:45,930
Warsaw LQG: So,
406
00:46:48,450 --> 00:46:58,260
Warsaw LQG: So on the all of the surface. That's funny. The, the neighborhood of the horizon. We use exactly the same rescaling as the as the horizon, so we can make
407
00:47:00,360 --> 00:47:08,040
Warsaw LQG: The horizon and the the past or future neighborhood one singular simultaneously with their horizon.
408
00:47:15,060 --> 00:47:16,260
Warsaw LQG: Yes. So, so
409
00:47:18,600 --> 00:47:23,040
Warsaw LQG: So that was our main results that we will cover this
410
00:47:25,230 --> 00:47:28,590
Warsaw LQG: Condition for the non singularity and then salted
411
00:47:29,790 --> 00:47:40,980
Warsaw LQG: So it's so you can see the first, the general case of the kernel space time privatized by massacre perimeter not parameter and lambda
412
00:47:44,130 --> 00:47:50,100
Warsaw LQG: We examine the geometry of the non generic horizon. And what we found is that
413
00:47:52,560 --> 00:48:01,980
Warsaw LQG: Consistent with the previous previous statements in the literature, generally, but the general generic values of the parameters the singularity is
414
00:48:04,140 --> 00:48:08,130
Warsaw LQG: Non removable in at least one of the and the polls.
415
00:48:10,620 --> 00:48:16,950
Warsaw LQG: Then we will post this condition down to the radius that the ratio of the circumference
416
00:48:18,000 --> 00:48:23,550
Warsaw LQG: And the ratio of the loops around the rotational axis as to tend to two pi.
417
00:48:25,380 --> 00:48:43,440
Warsaw LQG: In the polls. These gave us the condition for removing the singularity, which we solve and obtain the new and new solution. So this constraint lambda equals two free over a squared plus two squared plus two, or zero squared.
418
00:48:44,880 --> 00:48:50,640
Warsaw LQG: So that was our new result and also our conditional recovered the previous know
419
00:48:52,200 --> 00:48:53,730
Warsaw LQG: The previously known singer.
420
00:48:56,160 --> 00:48:57,240
Warsaw LQG: Solutions. So
421
00:48:58,350 --> 00:49:04,500
Warsaw LQG: Curve the theater space times and not the center around like to sit there your space times
422
00:49:05,850 --> 00:49:06,300
Warsaw LQG: And
423
00:49:10,260 --> 00:49:13,710
Warsaw LQG: Just think, fear is that there is still this
424
00:49:15,990 --> 00:49:19,410
Warsaw LQG: somewhat surprising for us part that
425
00:49:22,140 --> 00:49:31,530
Warsaw LQG: We can also we can make at least at most one of the horizon, no singular at the time because our constraints explicitly
426
00:49:32,850 --> 00:49:36,060
Warsaw LQG: Depends on the value or the radius of their horizon.
427
00:49:39,630 --> 00:49:43,770
Warsaw LQG: So next we we consider also
428
00:49:45,150 --> 00:49:50,400
Warsaw LQG: The neighborhood of the non singular prisons. So employed the framework of the
429
00:49:51,720 --> 00:49:52,860
Warsaw LQG: Space of the
430
00:49:53,940 --> 00:49:55,170
Warsaw LQG: orbits of the healing.
431
00:49:56,430 --> 00:49:58,740
Warsaw LQG: Vector developing the horizon.
432
00:49:59,850 --> 00:50:03,870
Warsaw LQG: And we found that it has a good properties in the known external case.
433
00:50:06,450 --> 00:50:12,810
Warsaw LQG: But we have to restrict ourselves to some small neighborhood of the horizon.
434
00:50:14,160 --> 00:50:15,660
Warsaw LQG: It should be zero here.
435
00:50:17,670 --> 00:50:20,520
Warsaw LQG: And then our metric metric
436
00:50:22,140 --> 00:50:27,960
Warsaw LQG: On the model space is well defined and has the signature. Not that we want actually
437
00:50:29,370 --> 00:50:36,060
Warsaw LQG: So our neighbors was his the topology of a sweet time some some interval around
438
00:50:37,620 --> 00:50:45,120
Warsaw LQG: Around the horizon. And in fact, each of the horizon has the topology of the abandoned.
439
00:50:46,260 --> 00:50:47,790
Warsaw LQG: Over, over a stone.
440
00:50:50,490 --> 00:50:51,120
Warsaw LQG: So,
441
00:50:53,910 --> 00:50:59,910
Warsaw LQG: I will research as I, as I said in the beginning, originated from from the quest to find
442
00:51:01,560 --> 00:51:02,400
Warsaw LQG: To to embed
443
00:51:03,420 --> 00:51:11,610
Warsaw LQG: All of the type deep, but from the path of typing and vacuum isolated horizons, which were
444
00:51:15,120 --> 00:51:15,630
Warsaw LQG: Which were
445
00:51:18,120 --> 00:51:22,950
Warsaw LQG: Found in some more abstract way we wanted to
446
00:51:23,970 --> 00:51:30,750
Warsaw LQG: To know how they correspond to into the unknown metrics. How are they embeddable
447
00:51:31,920 --> 00:51:36,300
Warsaw LQG: And Don'ts horizons on and non trivial to political bundle.
448
00:51:38,160 --> 00:51:40,410
Warsaw LQG: There were four dimensional family.
449
00:51:41,610 --> 00:51:42,660
Warsaw LQG: And because
450
00:51:44,100 --> 00:51:44,670
Warsaw LQG: Our
451
00:51:46,590 --> 00:52:02,880
Warsaw LQG: Our horizons are not singular only if we pull someone constraint on the cosmetic constant. We only have a three dimensional sub family. So the next quite obvious question is, was about the remaining time horizons and
452
00:52:06,360 --> 00:52:12,600
Warsaw LQG: We what we consider next where the accelerated cannot enter the Sitter space time
453
00:52:14,100 --> 00:52:28,020
Warsaw LQG: So one course, one can interpret the space time as a min similarity to the case of the current not under this space time but the black hole is also some some acceleration
454
00:52:30,000 --> 00:52:35,520
Warsaw LQG: Along the singular access and does it gives us a new degree of freedom.
455
00:52:38,070 --> 00:52:40,260
Warsaw LQG: Which we conjecture that can be
456
00:52:41,610 --> 00:52:51,750
Warsaw LQG: Connected to the fourth fourth dimensional and fourth dimension on this family have better update Dean biking horizon some some mantra that bundle.
457
00:52:54,720 --> 00:53:01,440
Warsaw LQG: And in fact, when we consider this case we arrived at exactly the same condition.
458
00:53:02,730 --> 00:53:05,190
Warsaw LQG: For the removing removing of
459
00:53:07,200 --> 00:53:08,220
Warsaw LQG: Of the singularity.
460
00:53:11,430 --> 00:53:16,710
Warsaw LQG: We employed the same framework we arrived at the end result that was formerly the same
461
00:53:18,060 --> 00:53:26,880
Warsaw LQG: So remember this condition constrained with with p zero P of by. So, this condition is the same.
462
00:53:27,960 --> 00:53:28,740
Warsaw LQG: But
463
00:53:30,000 --> 00:53:35,790
Warsaw LQG: The form of this P function diverse it's somewhat more complicated for the accelerated case.
464
00:53:37,110 --> 00:53:39,360
Warsaw LQG: And we also solve this
465
00:53:43,170 --> 00:53:55,500
Warsaw LQG: So this constraint and right there's some four dimensional family of accelerated current not on data center space time that meetings non singular horizons and neighborhoods and
466
00:53:57,210 --> 00:54:04,950
Warsaw LQG: Here there's an additional benefit that the constraint that we should have a positive because Minister constant, this
467
00:54:07,440 --> 00:54:12,060
Warsaw LQG: Is relaxed. So we don't mean some some negative customer for constant also
468
00:54:13,590 --> 00:54:14,070
Warsaw LQG: So,
469
00:54:15,630 --> 00:54:19,800
Warsaw LQG: More details about our methods about our resolve.
470
00:54:21,150 --> 00:54:27,240
Warsaw LQG: should appear in the upcoming paper some some time, we have this mouth and
471
00:54:28,560 --> 00:54:31,740
Warsaw LQG: It was not the answer questions. Thanks. Thank you for your attention.
472
00:54:55,980 --> 00:54:56,700
Penn State: No. Can you hear me.
473
00:54:58,200 --> 00:54:59,010
Warsaw LQG: I can hear you now.
474
00:54:59,940 --> 00:55:04,110
Penn State: Okay, so this is like a couple questions. The first is
475
00:55:05,280 --> 00:55:07,170
Penn State: If you go back to slide 14
476
00:55:09,870 --> 00:55:15,780
Penn State: Yeah, so you're looking for known singular certain non non solutions are, I guess.
477
00:55:16,800 --> 00:55:21,630
Penn State: It's like 30 you're looking at non singular solutions solutions with non single horizons. Right.
478
00:55:22,110 --> 00:55:30,240
Penn State: 13 or 1413 you're looking at general conditions you wrote down the slide. You're all done. And then in the next slide.
479
00:55:30,270 --> 00:55:30,930
Warsaw LQG: 14
480
00:55:31,230 --> 00:55:33,570
Penn State: Years give non non singular solutions.
481
00:55:34,860 --> 00:55:36,780
Penn State: Why so what happens to
482
00:55:39,480 --> 00:55:42,000
Penn State: The Singularity persistent. What's the story.
483
00:55:42,330 --> 00:55:46,500
Warsaw LQG: Yes incarnate. You cannot remove the singularity. Okay.
484
00:55:47,400 --> 00:55:47,760
Thank you.
485
00:55:49,530 --> 00:55:57,390
Penn State: The product question is the following that. I don't know if I understood the main message but i mean you know your result is that
486
00:55:58,590 --> 00:55:59,640
Penn State: Let's consider this
487
00:56:00,750 --> 00:56:10,170
Penn State: This for parameter family of solutions. And of course, it is of interest to consider the case where the generic case where none of the parameters is zero right
488
00:56:11,010 --> 00:56:11,340
Warsaw LQG: Yes.
489
00:56:11,610 --> 00:56:13,230
Penn State: And then in that case, sort of,
490
00:56:14,400 --> 00:56:18,870
Penn State: Your results implied that whether the cosmology of constant is positive or negative.
491
00:56:19,890 --> 00:56:21,780
Penn State: There is no way to get rid of.
492
00:56:22,800 --> 00:56:25,290
Penn State: The conical singularity on all the prizes.
493
00:56:28,320 --> 00:56:31,590
Warsaw LQG: Yes. So our clustering depends on the radio surprising sober, I
494
00:56:33,720 --> 00:56:34,320
Penn State: Might be able to
495
00:56:34,350 --> 00:56:40,770
Penn State: Choose your parameters and I mean if you like can be thought of as r&r or not depends on everything else.
496
00:56:42,270 --> 00:56:45,240
Penn State: So you can choose your parameters MN lambda
497
00:56:47,550 --> 00:56:47,850
And
498
00:56:49,860 --> 00:56:53,910
Penn State: L an A. Yeah, so you can choose those parameters, such that
499
00:56:56,730 --> 00:57:03,210
Penn State: Such that one or eyes and everything is fine, but then something will be wrong adopt another reason normally one sort of
500
00:57:04,380 --> 00:57:11,970
Penn State: Physically one is interested in solutions which don't have Monica singularities. Anyway, that was the main point of it. Is there any other people. Right.
501
00:57:12,480 --> 00:57:20,100
Penn State: Because of our clinical singularity is that means that there is a Einstein's equation or some stress any answer which corresponds to membrane no order.
502
00:57:21,630 --> 00:57:22,920
Penn State: So then
503
00:57:23,940 --> 00:57:26,730
Penn State: My take home message I took it to be that
504
00:57:28,500 --> 00:57:34,800
Penn State: The case with all four parameters non zero is physically not interesting. Am I missing something.
505
00:57:40,890 --> 00:57:41,130
Warsaw LQG: In
506
00:57:41,340 --> 00:57:43,980
Penn State: This case, irrespective of the sign of the cosmos actual cost and
507
00:57:45,330 --> 00:57:49,350
Penn State: It will be Hanukkah singularity is somewhere in the space time
508
00:57:50,460 --> 00:57:56,340
Warsaw LQG: It's so surprising results for us. Also, we also don't fully understand
509
00:57:58,320 --> 00:57:59,730
Warsaw LQG: Why this is the case.
510
00:58:01,110 --> 00:58:03,120
Warsaw LQG: Especially the the reason
511
00:58:03,840 --> 00:58:05,550
Penn State: Why this is the case, I'm just saying that if
512
00:58:06,060 --> 00:58:08,250
Penn State: Assuming that this is the case, which is your result.
513
00:58:08,850 --> 00:58:14,700
Penn State: Then I will just conclude that, that, that, that is, it implies that therefore
514
00:58:15,750 --> 00:58:16,170
The
515
00:58:17,850 --> 00:58:21,690
Penn State: Space times with all for panorama does not equal to zero or physically not interesting.
516
00:58:22,890 --> 00:58:30,840
Penn State: Because they will always have some why single I mean this sheet of singularity right this conical singularity between
517
00:58:32,340 --> 00:58:33,210
Penn State: idolizes
518
00:58:36,510 --> 00:58:38,220
Warsaw LQG: Results in place, right.
519
00:58:38,790 --> 00:58:39,390
Penn State: So you can hear.
520
00:58:39,480 --> 00:58:39,660
Penn State: Me.
521
00:58:39,720 --> 00:58:43,920
FAU Erlangen: And I can I can I help much, much, you can also
522
00:58:44,250 --> 00:58:58,230
FAU Erlangen: Yeah please elaborate on your question. Okay, so, so this is the zero to order conclusion that that this singularity cannot be removed all space. I mean, now this
523
00:58:59,250 --> 00:59:08,130
FAU Erlangen: peculiar property. Is that still for some special a choice of the cosmological constant
524
00:59:09,210 --> 00:59:16,500
FAU Erlangen: In neighborhood. One of the horizons becomes non singular and and its neighborhood is also
525
00:59:18,240 --> 00:59:23,370
FAU Erlangen: So, well, maybe it's not enough for you if you would like all the space time to be
526
00:59:23,970 --> 00:59:32,160
Penn State: Yeah, because that's what anybody would say, right, anybody would say that if I want to take the space time. Can you speak to be interesting. It is not enough that one neighborhood is this
527
00:59:32,670 --> 00:59:36,840
FAU Erlangen: So it depends on who we're talking to, if somebody is not interested in
528
00:59:40,260 --> 00:59:41,640
Nothing interesting
529
00:59:43,980 --> 00:59:46,620
Penn State: Exactly. The question I wanted to answer.
530
00:59:47,520 --> 00:59:52,950
FAU Erlangen: It is in between subtlety that are those horizons in
531
00:59:54,180 --> 01:00:04,200
FAU Erlangen: This Theater, which in some special for the values of cosmological constant are in non singular and also they are surrounded by non singular
532
01:00:04,980 --> 01:00:18,330
FAU Erlangen: Neighborhood. But let me also say something more. So in fact, we show that we're results to people who who are who wrote earlier some papers on not
533
01:00:18,900 --> 01:00:31,860
FAU Erlangen: Space times is actually our statement that generically those horizons have this unremovable clinical singularity is not something which is commonly
534
01:00:32,790 --> 01:00:46,440
FAU Erlangen: Believed and understood, people usually think that the singularity follows because of this non trivial topological character. And if we properly.
535
01:00:46,830 --> 01:00:53,130
FAU Erlangen: Glue space time then we grew one singular part was another non singular part and we
536
01:00:54,030 --> 01:01:01,260
FAU Erlangen: Don't have singularity at all. This is I think Mark Mars, send us the reference to some paper in which
537
01:01:01,560 --> 01:01:09,570
FAU Erlangen: This is explicitly stated, however, nobody proves this is just written as some remark that obviously if we create space I'm that we don't have
538
01:01:10,080 --> 01:01:32,700
FAU Erlangen: This clinical singularity. So, so the generic. So this take home message which you want to take it is also something something new because you may find statements in literature that actually there is no clinical singularity. If you properly. A extend this space time by this political glue
539
01:01:35,760 --> 01:01:38,760
Penn State: So is that true that, in this case, then if you
540
01:01:40,350 --> 01:01:43,650
Penn State: Have appropriate political identifications you can remove
541
01:01:45,300 --> 01:01:54,330
Penn State: The clinical singularity everywhere in space time when in the, in the case that is on the, on the, on the slide right night right now, which is that none of the parameters is equal to zero.
542
01:01:55,980 --> 01:01:59,760
FAU Erlangen: Know, I will resolve shows you can have
543
01:02:00,150 --> 01:02:12,660
Penn State: Yeah, so right so sauce. So I'm still don't understand. You said that you talked to some people and they were saying that this is a space types of physical interest and I'm very curious to know
544
01:02:14,730 --> 01:02:16,710
Penn State: What would be the physical application.
545
01:02:22,620 --> 01:02:27,000
FAU Erlangen: Well, this is a good, good question. I, I'm not sure.
546
01:02:28,890 --> 01:02:45,180
Penn State: So I just wanted to say that, you know, many, many years ago, I looked at also the the see metric, which has clinical singularity generically. It has parameters which is mass acceleration. And you can also enter the charge. And if you're all these see
547
01:02:46,260 --> 01:02:57,900
Penn State: Charges nonzero bed. In fact, you can do exactly what we have here on this slide. Maybe you can choose a particular value of charge, which is given by the other parameters, such that there is no clinical singularity.
548
01:02:59,160 --> 01:03:09,300
Penn State: But in that case it is there's no clinical singularity anywhere is based on that because they just to black hole. So it's not so complicated, like a cosmological horizon some black hole arises and so
549
01:03:10,950 --> 01:03:18,720
Penn State: So I think that's that's the reason why I'm very interested in this because it looked to me that it has some features like the charge symmetric
550
01:03:20,310 --> 01:03:30,750
Penn State: Okay. And the question was what along the way, did you learn anything striking or interesting or just as a side remark about the courtesy to our case.
551
01:03:32,040 --> 01:03:33,720
Penn State: You know those eloquent zero case.
552
01:03:37,650 --> 01:03:47,370
Warsaw LQG: So our patients and this is constantly reminds us that they don't work for the lambda zero and so
553
01:03:48,840 --> 01:03:50,070
Warsaw LQG: So I think that no
554
01:03:52,800 --> 01:03:53,610
Okay, thank you.
555
01:03:54,660 --> 01:03:55,020
Warsaw LQG: Thank you.
556
01:03:57,330 --> 01:04:02,220
Gravity Group, Univ. Wroclaw: Hello. So what is something maybe from the side. Let me get a little car from rosov
557
01:04:03,060 --> 01:04:03,330
Out.
558
01:04:04,650 --> 01:04:24,630
Gravity Group, Univ. Wroclaw: Okay, so I would like to learn more about your constraint between cosmological constant, this, this condition with our zero square where it came from. You said that gluing is not enough. So this is some kind of differentiable result, I don't know, like how to this and where you got this
559
01:04:28,980 --> 01:04:30,930
Warsaw LQG: So you're talking about this condition.
560
01:04:30,960 --> 01:04:32,400
Gravity Group, Univ. Wroclaw: Yes, yes.
561
01:04:32,460 --> 01:04:33,060
Warsaw LQG: Yes, exactly.
562
01:04:34,710 --> 01:04:35,490
Warsaw LQG: So, it
563
01:04:36,660 --> 01:04:39,750
Warsaw LQG: Comes from solving this this equation.
564
01:04:40,920 --> 01:04:44,010
Warsaw LQG: This constraint which which to arrive at by
565
01:04:44,790 --> 01:04:45,840
Warsaw LQG: Requiring that
566
01:04:45,960 --> 01:04:48,150
Warsaw LQG: The limit is to buy
567
01:04:49,980 --> 01:04:55,530
Gravity Group, Univ. Wroclaw: So this is just some kind of consistency condition between on two poles.
568
01:04:55,980 --> 01:04:58,890
Gravity Group, Univ. Wroclaw: Yes, somebody with some kind of light colored say
569
01:05:00,030 --> 01:05:05,250
Gravity Group, Univ. Wroclaw: One expression multiplying P pie and another expression multiplying p zero
570
01:05:06,480 --> 01:05:18,600
Gravity Group, Univ. Wroclaw: So it's some kind of consistency condition between the polls, because let me say a couple reminders, because I was playing in the past about hope not. Space name. He also had one slide with my
571
01:05:19,050 --> 01:05:41,070
Gravity Group, Univ. Wroclaw: My work. So basically, I noticed that behavior of this strings to be somehow like representing a rotation like basically you can have another set of killing vectors and just consider that you have a constant angular velocity and then that explains somehow why this taupe
572
01:05:42,210 --> 01:05:51,840
Gravity Group, Univ. Wroclaw: List is not parameter actually is very similar to the care parameter in the formulas. Somehow it like a represents that projection on busy access even
573
01:05:52,110 --> 01:06:04,200
Gravity Group, Univ. Wroclaw: When you look closer to the formulas and basically along the way I wanted to, to, to leave this to canonical a clinical singularities basically
574
01:06:04,710 --> 01:06:11,400
Gravity Group, Univ. Wroclaw: Represent the black hole peers five at cosmic string, which was rotating or to cosmic strings rotating
575
01:06:11,970 --> 01:06:28,590
Gravity Group, Univ. Wroclaw: And then basically, I wanted to leave this space them as it is hoping that I will get some kind of maybe another kind of condition consistency condition which would like avoid glowing about maybe along the way, having something. So you have some kind of condition which looks
576
01:06:29,820 --> 01:06:38,100
Gravity Group, Univ. Wroclaw: In the, in the service philosophy, but you want always to remove this severity. So it's like Mark
577
01:06:38,850 --> 01:06:42,840
Warsaw LQG: Is also, we do want to make this glowing
578
01:06:43,320 --> 01:06:44,700
Warsaw LQG: Hmm, contrary to
579
01:06:46,140 --> 01:06:47,100
Warsaw LQG: What you're trying to do.
580
01:06:48,030 --> 01:07:00,660
Gravity Group, Univ. Wroclaw: I just wanted to do, like, see what what is possible to learn more about this metric, as it is right along the way. I don't have any conclusions, but I notice couple of of really strange kind of papers.
581
01:07:01,740 --> 01:07:08,940
Gravity Group, Univ. Wroclaw: Really like the rotation rotating character of this kind of things, not only the kind of like mass parameters stuff.
582
01:07:12,660 --> 01:07:30,120
FAU Erlangen: I would like to add something to the reply which magic, magic sauce. So the question was what is actually non singular if we still can glue do gluing of two to two sections. So, in
583
01:07:30,930 --> 01:07:44,370
FAU Erlangen: Our space time couple logically has structure on this hub bundle times some to other dimensions which I can tractable, so they don't make topology. They don't change anything, and now
584
01:07:45,450 --> 01:07:55,230
FAU Erlangen: There are some objects on on bundle which are engaged set gauge dependent or section dependent. However, there are some structures which are
585
01:07:55,680 --> 01:08:06,960
FAU Erlangen: Independent and would we consider is the space of fibers and the space of fibers is geometric object that this is a choice of slice independent
586
01:08:07,620 --> 01:08:21,840
FAU Erlangen: And if this space of fibers has a problem has some differential ability then choosing sections is not helping so so space of fibers is this invariant object.
587
01:08:22,710 --> 01:08:36,270
FAU Erlangen: Is defined in independently on on choice of coordinates. So we consider. So the bottom line is we consider some property, which is independent of choice of coordinates.
588
01:08:42,390 --> 01:08:43,410
Jorge Pullin: Any other questions.
589
01:08:46,380 --> 01:08:47,880
FAU Erlangen: Actually I have I have still
590
01:08:48,960 --> 01:08:55,200
FAU Erlangen: Answer, maybe, maybe some extension of my answer, which I gave to buy. So I buys
591
01:08:57,360 --> 01:09:07,530
FAU Erlangen: A conclusion from this, from this result was that it because, as we say space time can be made non singular only in the
592
01:09:08,250 --> 01:09:20,580
FAU Erlangen: At most, for one horizon and only neighborhood of this horizon. So it is not physically. It cannot be physically interesting I think this is not something which we check that.
593
01:09:21,030 --> 01:09:34,110
FAU Erlangen: Actually, it can happen for the outer most horizon. So if we if this outermost horizon is non singular, then it's possible that maybe we can extend this
594
01:09:34,950 --> 01:09:43,470
FAU Erlangen: We can remove singularity, all the way from from this horizon to to to all the for all the values of
595
01:09:44,010 --> 01:09:58,710
FAU Erlangen: Of our, of course, still those cabinet space times have they another simplistically flights. So, so I can say, we can do it all the way to describe, but we can do it all the way to infinity of our perhaps this is a construction.
596
01:10:00,270 --> 01:10:08,010
Penn State: Thank you. First of all, thank you very much for your clarification, with the previous clarification, which is that that what you're doing is on the on the space of
597
01:10:09,360 --> 01:10:13,890
Penn State: Generators. And so that really is very important time in that. And that's why
598
01:10:15,930 --> 01:10:29,340
Penn State: Not because if the space generators singularity is much more serious than some cross section is it so thank you for your last answer. The point is that such a space, time, and even
599
01:10:31,020 --> 01:10:31,440
Penn State: The sitter.
600
01:10:34,440 --> 01:10:48,330
Penn State: Would have many several prizes. So just looking so what will happen is that just to get out to most wonders interesting that, then the exterior of the outermost is perfectly fine, but then there will be
601
01:10:49,410 --> 01:11:04,680
Penn State: Kind of kind of comical singularity is in between the two other horizons. Right. I mean, you can you go through your reasons. And so the statement is that they'll be conical singularity in the two other lines, but maybe what you would like to say something like
602
01:11:05,940 --> 01:11:09,060
Penn State: For some reason, physical reason you might be able to argue that
603
01:11:10,350 --> 01:11:11,040
Penn State: Only the
604
01:11:12,060 --> 01:11:24,330
Penn State: The part outside the outermost horizon is what is of interest, but you have to check if that horizon as a cosmological horizon, or is it a black hole of horizon, or what kind of horizon, it is or is a new kind of. So thank you very much.
605
01:11:24,570 --> 01:11:33,570
FAU Erlangen: Yes, yes, that's true, that this is outermost horizon may well be a cosmological horizon and this is also something we don't know for sure.
606
01:11:37,800 --> 01:11:38,670
Jorge Pullin: Any more questions.
607
01:11:39,150 --> 01:11:43,530
Gravity Group, Univ. Wroclaw: Whether you want to have you look at hyperbolic version of because
608
01:11:44,400 --> 01:11:56,640
Gravity Group, Univ. Wroclaw: The paper by Robert month where they consider playing with hyperbolic coconut and some kind of special limits were not parameter has like a cosmological constant
609
01:11:57,630 --> 01:12:16,530
Gravity Group, Univ. Wroclaw: Expression and then there is some kind of duality with like a care. So this hyper bowling one have minuses in some places and that allowing you to kind of certain limits that something is going away. But basically, there is a relation between not parameter and cosmological constant
610
01:12:18,210 --> 01:12:20,430
Gravity Group, Univ. Wroclaw: So that's it. Have you, have you look at it, summer.
611
01:12:21,480 --> 01:12:28,650
Gravity Group, Univ. Wroclaw: Consider if it doesn't change something, if you have another relation between an a parameter and cosmological constant
612
01:12:30,750 --> 01:12:35,130
Warsaw LQG: Well, we haven't looked at this work actually so so
613
01:12:36,360 --> 01:12:37,950
Warsaw LQG: On the fire on the answer.
614
01:12:38,520 --> 01:12:39,330
Warsaw LQG: Would change.
615
01:12:40,950 --> 01:12:44,400
Warsaw LQG: If you can send us that will look at it. Okay.
616
01:12:44,670 --> 01:12:45,420
Warsaw LQG: This paper.
617
01:12:46,560 --> 01:12:59,280
FAU Erlangen: And didn't work in that work is the shape of slice of the horizon is all the while this horizon is a bundle over to or
618
01:12:59,310 --> 01:13:00,870
Gravity Group, Univ. Wroclaw: Over some some
619
01:13:01,620 --> 01:13:13,980
Gravity Group, Univ. Wroclaw: I just like, I don't really need it, but it was not care, too. I like Ultra spinning terror on this another side of duality. So I don't know exactly what is whether you send the paper and hopefully
620
01:13:16,800 --> 01:13:17,100
FAU Erlangen: Thanks.
621
01:13:21,360 --> 01:13:21,990
Jorge Pullin: Anything else
622
01:13:26,520 --> 01:13:27,870
Jorge Pullin: Okay, let's thank the speaker again.