Gravitational radiation in high speed black hole collisions. 1. Perturbation treatment of the axisymmetric speed of light collision
Mar 10, 199262 pages
Published in:
- Phys.Rev.D 46 (1992) 658-674
Report number:
- DAMTP-R-92-4
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Abstract: (APS)
In this and the two following papers II and III we study the axisymmetric collision of two black holes at the speed of light, with a view to understanding the more realistic collision of two black holes with a large but finite incoming Lorentz factor γ. The curved radiative region of the space-time, produced after the two incoming impulsive plane-fronted shock waves have collided, is treated using perturbation theory, following earlier work by Curtis and Chapman. The collision is viewed in a frame to which a large Lorentz boost has been applied, giving a strong shock with energy ν off which a weak shock with energy λ≪ν scatters. This yields a singular perturbation problem, in which the Einstein field equations are solved by expanding in powers of λ/ν around flat space-time. When viewed back in the center-of-mass frame, this gives a good description of the regions of the space-time in which gravitational radiation propagates at small angles θ^ but a large distance from the symmetry axis, near each shock as it continues to propagate, having been distorted and deflected in the initial collision. The news function c0(τ^,θ^) describing the gravitational radiation is expected to have a convergent series expansion c0(τ^,θ^) =tsumn=0∞a2n(τ^)sin2nθ^, where τ^ is a retarded time coordinate. First-order perturbation theory gives an expression for a0(τ^) in agreement with that found previously by studying the finite-γ collisions. Second-order perturbation theory gives a2(τ^) as a complicated integral expression.
A new mass-loss formula is derived, which shows that if the end result of the collision is a single Schwarzschild black hole at rest, plus gravitational radiation which is (in a certain precise sense) accurately described by the above series for c0(τ^,θ^), then the final mass can be determined from knowledge only of a0(τ^) and a2(τ^). This leads to an interesting test of the cosmic censorship hypothesis. The numerical calculation of a2(τ^) is made practicable by analytical simplifications described in the following paper II, where the perturbative field equations are reduced to a system in only two independent variables. Results are presented in the concluding paper III, which discusses the implications for the energy emitted and the nature of the radiative space-time.- black hole: scattering
- scattering: black hole
- gravitational radiation
- symmetry: axial
- perturbation theory
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