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Black-hole evaporation and the equivalence principle.

This article investigates the underlying physics of Hawking radiation. It is proposed that global quantum field theory on the Schwarzschild background is such that its restriction to any point of spacetime is consistent with the field theory postulated by a freely falling observer at that point. The equivalence principle demands that the field theory defined by freely falling observers be the same as special relativisitic (flat-spacetime) field theory in a neighborhood of the observer. A minor technical point is that one needs to find a family of freely falling observers whose world lines form a space-filling congruence in order to synthesize the theory. Once this is accomplished, the global field theory as dictated by the equivalence principle predicts that a black hole experiences thermal evaporation in isolation. The main point of this paper is to attain a physical understanding of this phenomenon with particular emphasis on the renormalized stress-energy tensor. It is shown that this tensor is a measure of the change in the energy of the zero-point oscillations of the field theory which is formulated by inertial observers during free fall, as compared to a global standard. An external onlooker sees the zero-point energy in a freely falling coordinate patch decrease as it approaches the horizon. The freely falling coordinate patch was assigned a value of zero renormalized energy due to the oscillations of the field when it was released from rest near ``infinity'' in the distant past. This decrease in zero-point energy during free fall is shown to translate to a negative energy density of the field, near the horizon, in the components of the renormalized stress-energy tensor. The external onlooker interprets the zero-point energy lost during free fall as an outgoing stream of particle-antiparticle pairs.