COMPLEX ANGULAR-MOMENTUM APPROACH TO BLACK-HOLE SCATTERING

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 lambda(= l + 1/2)-plane. We also show that the S-matrix possesses a global symmetry relation S(-lambda) = e-2ipi(lambda)S(lambda), 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.