Approximate stress-energy tensor for evaporating black holes.

Abstract

We approximate the Israel-Hartle-Hawking and Unruh stress-energy tensors of quantum fields in the neighborhood of a static Schwarzschild black hole. The approximate tensors are constructed from the conservation equations in the ultrastatic optical metric of the black hole and the expected regularity properties at the horizon, in the respective vacua. Our scheme reproduces the approximation of Page, Brown, and Ottewill for the Israel-Hartle-Hawking vacuum and yields a tensor for the Unruh state. The latter exhibits the correct behavior at infinity and predicts luminosities in good agreement with numerical calculations.