  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.

Astrophysics