# Boson Stars Collisions

Let us consider binary bosons stars which are described with the same global
scalar field φ.
The initial data is constructed by simple superposition

φ = φ_{1}(**r**-**r**_{1},**v**_{1})
+ φ_{2}(**r**-**r**_{2},**v**_{2})

being φ_{i} the initial data for the single boson star i centered
at **r**_{i} and boosted with a speed **v**_{i}.
The U(1) symmetry allows to introduce modifications on the imaginary part of the
scalar field solution, so we will consider

φ_{1} = φ_{0}(**r**)
e^{ i ϖ t }

φ_{2} = φ_{0}(**r**)
e^{ i ε ϖ t + θ }

where ε = +1 corresponds to a boson star and ε = -1 to an antiboson one.
Notice that there can be also a phase difference θ between the stars.

## Head-on collisions

- Boson/boson pair (ε = +1, θ = 0)
- Metric component g
_{11}
- Scalar field φ

- Boson/boson in opposition of phase pair (ε = +1, θ = π)
- Metric component g
_{11}
- Scalar field φ

## Orbiting systems

- Boson/boson pair (ε = +1, θ = 0, J
_{z} = 0.8)
- energy density ρ

- Boson/boson pair (ε = +1, θ = 0, J
_{z} = 1.0)
- energy density ρ

- Boson/antiboson pair (ε = -1, θ = 0, J
_{z} = 0.8)
- energy density ρ

- Boson/antiboson pair (ε = -1, θ = 0, J
_{z} = 1.0)
- energy density ρ

- Boson/boson in opposition of phase pair (ε = +1, θ = π , J
_{z} = 1.0)
- energy density ρ

## Parameter survey for the orbiting boson/boson pair

- v= 0.0 : head on collision forming a black hole
- energy density ρ

- v= 0.052 : merge into a rotating bar which splits in two pieces
- energy density ρ
- Scalar field φ (log scale)

- v= 0.064 : merge into a rotating bar which disperses scalar field
- energy density ρ
- Scalar field φ (log scale)

- v= 0.072 : merge into a rotating bar which bounds until form a black hole
- energy density ρ
- Scalar field φ (log scale)

- v= 0.082 : merge into a kerr black hole
- energy density ρ
- Scalar field φ (log scale)