A Model for Evaporating Black Holes

Abstract

We consider Vaidya's classical spacetime which represents a mass decreasing black hole by means of an inward energy flow. To consider the particle creation in such a spacetime, we try to know the change of the particle creation rate of the black hole without considering ba<;k·reaction problem. We construct a model which varies its mass like V-I (V the usual advanced null time) to find that the particle creation i.n this spacetime is divergent at the final stage. This result means that a real evaporating black hole is not represented by this model, and therefore suggests that the appearance of a zero mass naked singularity cannot be avoided. Hawking's discovery that a black hole formed by collapsing matter emits blackbody radiation whose temperature is proportional to its surface gravityl) is a great stimulus to the quantum field theory in curved spacetime. Though the original calculation of the Hawking radiation is done by assuming the stationariness of black hole, the black hole must reduce its mass by the requirement of the energy conservation. 7l Then it will be interesting to investigate the changing rate of the mass and the radiation of the black hole by considering back-reaction effect. To attack this problem straightforwardly, it is necessary to solve dynamically the semiclassical Einstein equations with the energy­ momentum tensor of the created particles as the source. However, this approach is technically very difficult. In view of this, as the first step to investigate the dynamical evolution of a radiating black hole, it will be worthwhile to study the particle creation on a classically fixed background spacetime representing a black hole with varing mass. The Vaidya metric 2 ) is known as such a spacetime. It has the form