The semiclassical back reaction to black hole evaporation (wherein the renormalized energy-momentum tensor is taken as a source of Einstein’s equations) is analyzed in detail. It is shown that, so long as the mass of a Schwarzschild black hole is greater than the Planck mass, it decreases according to Hawking’s law dM/dt=-C/${\mathit{M}}^2$, where C is a constant of order one, and the black hole emits particles with a thermal spectrum at temperature 1/8πM(t).

• Received 23 May 1995

DOI:https://doi.org/10.1103/PhysRevD.52.5857