Bounding the greybody factors for Schwarzschild black holes

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 center dot, deriving rigorous bounds on the greybody factors as a function of s, center dot, wave frequency omega, and the black-hole mass m.