Glory scattering by black holes.

Abstract

We present a physically motivated derivation of the JWKB backward glory-scattering cross section of massless waves by Schwarzschild black holes. The angular dependence of the cross section is identical with the one derived by path integration, namely, d\ensuremath{\sigma}/d\ensuremath{\Omega}=4${\ensuremath{\pi}}^{2}$${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$${B}_{g}$${}^{2}$(dB mW\ensuremath{\pi}, where \ensuremath{\lambda} is the wavelength, B(\ensuremath{\theta}) is the inverse of the classical deflection function CTHETA(B), ${B}_{g}$ is the glory impact parameter, s is the helicity of the scattered wave, and ${J}_{2s}$ is the Bessel function of order 2s. The glory rings formed by scalar waves are bright at the center; those formed by polarized waves are dark at the center. For scattering of massless particles by a spherical black hole of mass M, B(\ensuremath{\theta})/M\ensuremath{\sim}3 \ensuremath{\surd}3 +3.48 exp(-\ensuremath{\theta}), \ensuremath{\theta}>owig\ensuremath{\pi}. The numerical values of d\ensuremath{\sigma}/d\ensuremath{\Omega} for this deflection function are found to agree with earlier computer calculations of glory cross sections from black holes.