# 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 = φ1(r-r1,v1) + φ2(r-r2,v2)
being φi the initial data for the single boson star i centered at ri and boosted with a speed vi.
• The U(1) symmetry allows to introduce modifications on the imaginary part of the scalar field solution, so we will consider
φ1 = φ0(r)   e i ϖ t
φ2 = φ0(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.

1. Boson/boson pair (ε = +1, θ = 0)
1. Metric component g11
2. Scalar field φ
2. Boson/boson in opposition of phase pair (ε = +1, θ = π)
1. Metric component g11
2. Scalar field φ

## Orbiting systems

1. Boson/boson pair (ε = +1, θ = 0, Jz = 0.8)
1. energy density ρ
2. Boson/boson pair (ε = +1, θ = 0, Jz = 1.0)
1. energy density ρ
3. Boson/antiboson pair (ε = -1, θ = 0, Jz = 0.8)
1. energy density ρ
4. Boson/antiboson pair (ε = -1, θ = 0, Jz = 1.0)
1. energy density ρ
5. Boson/boson in opposition of phase pair (ε = +1, θ = π , Jz = 1.0)
1. energy density ρ

## Parameter survey for the orbiting boson/boson pair

1. v= 0.0 : head on collision forming a black hole
1. energy density ρ
2. v= 0.052 : merge into a rotating bar which splits in two pieces
1. energy density ρ
2. Scalar field φ (log scale)
3. v= 0.064 : merge into a rotating bar which disperses scalar field
1. energy density ρ
2. Scalar field φ (log scale)
4. v= 0.072 : merge into a rotating bar which bounds until form a black hole
1. energy density ρ
2. Scalar field φ (log scale)
5. v= 0.082 : merge into a kerr black hole
1. energy density ρ
2. Scalar field φ (log scale)