Gravitational radiation in black-hole collisions at the speed of light. I. Perturbation treatment of the axisymmetric collision
- 15 July 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 46 (2), 658-674
- https://doi.org/10.1103/physrevd.46.658
Abstract
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 (τ^,θ^) describing the gravitational radiation is expected to have a convergent series expansion (τ^,θ^) = (τ^)θ^, where τ^ is a retarded time coordinate. First-order perturbation theory gives an expression for (τ^) in agreement with that found previously by studying the finite-γ collisions. Second-order perturbation theory gives (τ^) as a complicated integral expression.
Keywords
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