Glory scattering by black holes

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, dσ/dΩ=4${\pi }^2$${\lambda }^{\mathrm{-}1}$$B_g$${}^2$(dB mWπ, where λ is the wavelength, B(θ) 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(θ)/M∼3 √3 +3.48 exp(-θ), θ>owigπ. The numerical values of dσ/dΩ for this deflection function are found to agree with earlier computer calculations of glory cross sections from black holes.