Ingoing Eddington-Finkelstein Metric of an Evaporating Black Hole

Abstract

We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.

Version published by Physical Review D, including 2018 data of Bardeen incorporated into improved results here, and also more discussion of the properties of the stress-energy tensors, such as showing for the first time that for a conformal massless scalar field, there is no timelike eigenvector anywhere outside the black hole, so the energy flux is outward for all observers of all velocities