Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole

Abstract

Hawking has predicted that a black hole will emit particles as if it had a temperature proportional to its surface gravity. This paper combines Hawking's quantum formalism with the black-hole perturbation methods of Teukolsky and Press to calculate the emission rate for the known massless particles. Numerical results indicate that a hole of mass $M\ensuremath{\gg}{10}^{17}$ g should emit a total power output of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{\hbar}{c}^{6}{G}^{\ensuremath{-}2}{M}^{\ensuremath{-}2}$, of which 81% is in neutrinos, 17% is in photons, and 2% is in gravitons. These rates plus an estimate for the emission rates of massive particles from smaller holes allow one to infer that a primordial black hole will have decayed away within the present age of the universe if and only if its initial mass was $M<(5\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{14}$ g.