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The back reaction effect in particle creation in curved spacetime. (English) Zbl 1173.81328
Summary: 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 operator \(T_{\nu}\) should satisfy in order to give a reasonable semiclassical theory. It is proven that these conditions uniquely determine \(T_{\nu}\), 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 renormalizing \(T_{\nu}\). Modulo some standard assumptions which are made in defining the prescription for \(T_{\nu}\), it is shown that this prescription satisfies at least four of the five axioms.

MSC:
81T20 Quantum field theory on curved space or space-time backgrounds
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
53C80 Applications of global differential geometry to the sciences
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