#### 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 $M\gg {10}^{17}$ g should emit a total power output of $2\times {10}^{-4\mathrm{}}\hslash {c}^{6}{G}^{-2\mathrm{}}{M}^{-2\mathrm{}}$, 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 $M<(5\mathrm{}\pm 1)\times {10}^{14}$ g.

DOI: http://dx.doi.org/10.1103/PhysRevD.13.198

- Received 18 August 1975
- Published in the issue dated 15 January 1976

© 1976 The American Physical Society