Bounding the greybody factors for Schwarzschild black holes

Abstract

Greybody factors in black-hole physics modify the naive Planckian spectrum that is predicted for Hawking radiation when working in the limit of geometrical optics. We consider the Schwarzschild geometry in $(3+1)$ dimensions, and analyze the Regge-Wheeler equation for arbitrary particle spin $s$ and wave-mode angular momentum $\ensuremath{\ell}$, deriving rigorous bounds on the greybody factors as a function of $s$, $\ensuremath{\ell}$, wave frequency $\ensuremath{\omega}$, and the black-hole mass $m$.