Wave scattering theory and the absorption problem for a black hole
Abstract
The general problem of scattering and absorption of waves from a Schwarzschild black hole is investigated. A scattering absorption amplitude is introduced. The unitarity theorem for this problem is derived from the wave equation and its boundary conditions. The formulation of the problem, within the formal scattering theory approach, is also given. The existence of a singularity in spacetime is related explicitly to the presence of a nonzero absorption cross section. Another derivation of the unitarity theorem for our problem is given by operator methods. The reciprocity relation is also proved; that is, for the scattering of waves the black hole is a reciprocal system. Finally, the elastic scattering problem is considered, and the elastic scattering amplitude is calculated for high frequencies and small scattering angles.
 Publication:

Physical Review D
 Pub Date:
 August 1977
 DOI:
 10.1103/PhysRevD.16.937
 Bibcode:
 1977PhRvD..16..937S
 Keywords:

 Absorption Cross Sections;
 Black Holes (Astronomy);
 Field Theory (Physics);
 Schwarzschild Metric;
 Wave Scattering;
 Asymptotic Methods;
 Elastic Scattering;
 Gravitational Waves;
 Reciprocal Theorems;
 SpaceTime Functions;
 Wave Equations;
 Astrophysics