Boson star collisions in gr
This presentation is the property of its rightful owner.
Sponsored Links
1 / 22

Boson Star collisions in GR PowerPoint PPT Presentation


  • 49 Views
  • Uploaded on
  • Presentation posted in: General

Boson Star collisions in GR. ERE 2006 Palma de Mallorca, 6 September 2006. Carlos Palenzuela, I.Olabarrieta, L.Lehner & S.Liebling. I. Introduction. I. What is a Boson Star (BS)?.

Download Presentation

Boson Star collisions in GR

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Boson star collisions in gr

Boson Starcollisions in GR

ERE 2006

Palma de Mallorca, 6 September 2006

Carlos Palenzuela,

I.Olabarrieta, L.Lehner & S.Liebling


I introduction

I. Introduction


I what is a boson star bs

I. What is a Boson Star (BS)?

  • Boson Stars: compact bodies composed of a complex massive scalar field, minimally coupled to the gravitational field

  • - simple evolution equation for the matter

  •  it does not tend to develop shocks

  •  it does not have an equation of state


I motivation

I. Motivation

  • 1) model to study the 2 body interaction in GR

  • 2) candidates for the dark matter

  • 3) study other issues, like wave extraction, gauges, …


Ii the evolution equations

II. The evolution equations


Ii the ekg evolution system i

II. The EKG evolution system (I)

  • Lagrangian of a complex scalar field in a curved background (natural units G=c=1)

L = - R/(16 π) + [gabaφ* bφ + m2 |φ|2 /2 ]

  • R : Ricci scalar

  • gab : spacetime metric

  • φ, φ* : scalar field and its conjugate complex

  • m : mass of the scalar field


Ii ekg evolution system ii

II. EKG evolution system (II)

  • The Einstein-Klein-Gordon equations are obtained by varying the action with respect to gab and φ

  • - EE with a real stress-energy tensor (quadratic)

  • - KG : covariant wave equation with massive term

Rab = 8π (Tab – gab T/2)

Tab = [aφbφ* + bφ aφ* – gab (cφ cφ* + m2 |φ|2) ]/2

gaba bφ = m2φ


Ii the harmonic formalism

II. The harmonic formalism

  • 3+1 decomposition to write EE as a evolution system

  • - EE in the Dedonder-Fock form

  • - harmonic coordinates Γa = 0

□gab = …

  • Convert the second order system into first order to use

  • numerical methods that ensure stability (RK3, SBP,…)


Iii testing the numerical code

III. Testing the numerical code


Iii the numerical code

III. The numerical code

  • Infrastructure : had

  • Method of Lines with 3rd order Runge-Kutta to

  • integrate in time

  • Finite Difference space discretization satisfying

  • Summation By Parts (2nd and 4th order)

  • - Parallelization

  • Adaptative Mesh Refinement in space and time


Iii initial data for the single bs

III. Initial data for the single BS

1) static spherically symmetric spacetime in isotropic

coordinates

ds2 = - α2 dt2 + Ψ4 (dr2 + r2 dΩ2)

2) harmonic time dependence of the complex scalar field

φ = φ0(r) e-iωt

3) maximal slicing condition

trK = ∂t trK = 0


Iii initial data for the single bs ii

III. Initial data for the single BS(II)

  • Substitute previous ansatzs in EKG

  •  set of ODE’s, can be solved for a given φ0(r=0)

  •  eigenvalue problem for {ω : α(r), Ψ(r), φ0(r)}

  • - stable configurations for Mmax ≤ 0.633/m

φ0

gxx


Iii evolution of a single bs

III. Evolution of a single BS

φ = φ0(r) e-iωt

Re(φ) = φ0(r) cos(ωt)

  • The frequency and amplitude of the star gives us a good measure of the validity of the code (+ convergence)


Iv head on collisions of bs

IV. Head-on collisions of BS


Iv the 1 1 bs system

IV. The 1+1 BS system

  • Superposition of two single boson stars

  • φT = φ1 + φ2

  • ΨT = Ψ1 + Ψ2 - 1

  • αT = α1 + α2 - 1

  • - satisfies the constraints up to discretization error if the

  • BS are far enough


Iv the equal mass case

L=30

R=13

φ0(0)=0.01

ω = 0.976

M=0.361

φ0(0)=0.01

ω = 0.976

M=0.361

IV. The equal mass case

  • Superposition of two BS with the same mass


Iv the equal mass case1

IV. The equal mass case

|φ|2 (plane z=0) gxx (plane z=0)


Iv the unequal mass case

L=30

R=13

R=9

φ0(0)=0.03

ω = 0.933

M=0.542

φ0(0)=0.01

ω = 0.976

M=0.361

IV. The unequal mass case

  • Superposition of two BS with different mass


Iv the unequal mass case1

IV. The unequal mass case

|φ|2 (plane z=0) gxx (plane z=0)


Iv the unequal phase case

IV. The unequal phase case

  • Superposition of two BS with the same mass but a difference of phase of π

L=30

R=13

φ0(0)=0.01

ω = 0.976

M=0.361

φ0(0)=0.01

ω = 0.976

M=0.361

φ = φ0(r) e-iωt

φ = φ0(r) e-i(ωt+π)


Iv the unequal phase case1

IV. The unequal phase case

|φ|2 (plane z=0) gxx (plane z=0)


Future work

Future work

  • Develop analysis tools (wave extraction, …)

  • Analyze and compare the previous cases with BHs

  • Study the new cases that appear only in BS collisions


  • Login