Abstract
The problem of determining the changes in the gravitational field caused by particle creation is investigated in the context of the semiclassical approximation, where the gravitational field (i.e., spacetime geometry) is treated classically and an effective stress energy is assigned to the created particles which acts as a source of the gravitational field. An axiomatic approach is taken. We list five conditions which the renormalized stress-energy operatorT μv should satisfy in order to give a reasonable semiclassical theory. It is proven that these conditions uniquely determineT μv , i.e. there is at most one renormalized stress-energy operator which satisfies all the conditions. We investigate existence by examining an explicit “point-splitting” type prescription for renormalizingT μv . Modulo some standard assumptions which are made in defining the prescription forT μv , it is shown that this prescription satisfies at least four of the five axioms.
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Communicated by R. Geroch
Supported in part by the National Science Foundation under grant MPS 74-17456-A01 and by the Sloan Foundation
Sloan Foundation fellow
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Wald, R.M. The back reaction effect in particle creation in curved spacetime. Commun.Math. Phys. 54, 1–19 (1977). https://doi.org/10.1007/BF01609833
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DOI: https://doi.org/10.1007/BF01609833