Astronomy and Astrophysics – Astrophysics
Scientific paper
2005-04-27
Astronomy and Astrophysics
Astrophysics
18 pages, Revtex4. Submitted to Lecture Notes of S.I.M., volume edited by D. Cocolicchio and S. Dragomir, with kind permission
Scientific paper
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is here analyzed by studying the corresponding second-order hyperbolic operator with variable coefficients, instead of using the reduction method from the retarded flat-space Green function in four dimensions. After reduction to canonical form of this hyperbolic operator, the integral representation of the solution in terms of the Riemann function is obtained. The Riemann function solves a characteristic initial-value problem for which analytic formulae leading to the numerical solution are derived.
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