Complex angular momentum approach to black-hole scattering

Abstract

A description of scalar waves scattered off a Schwarzschild black hole is discussed in terms of complex angular momenta. In the new picture the scattering amplitude is split into a supposedly smooth background integral and a sum over the so-called Regge poles. It is proved that all the relevant Regge poles (the singularities of the S-matrix) must be situated in the first quadrant of the complex -plane. We also show that the S-matrix possesses a global symmetry relation , which makes it possible to simplify considerably the background integral. Finally, a formal basis for actual computations of Regge poles and the associated residues is outlined.