The Semi-Classical Back Reaction to Black Hole Evaporation

The semi-classical back reaction to black hole evaporation (wherein the renormalized energy momentum tensor is taken as source of Einstein's equations) is analyzed in detail. It is proven that the mass of a Schwarzshild black hole decreases according to Hawking's law $dM/dt = - C/ M^2$ where $C$ is a constant of order one and that the particles are emitted with a thermal spectrum at temperature $1/8\pi M(t)$.