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Linear Response and the Validity of the Semi-Classical Approximation in Gravity

Paul R. Anderson·Carmen Molina-Paris·Emil Mottola
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Abstract

We propose a quantitative test for the validity of the semi-classical approximation in gravity, namely that the solutions to the semi-classical equations should be stable to linearized perturbations, in the sense that no gauge invariant perturbation should become unbounded in time. We show that a self-consistent linear response analysis of these perturbations based upon an invariant effective action principle involves metric fluctuations about the mean semi-classical geometry and brings in the two-point correlation function of the quantum energy-momentum tensor in a natural way. The properties of this correlation function are discussed and it is shown on general grounds that it contains no state-dependent divergences and requires no new renormalization counterterms beyond those required in the leading order semi-classical approximation.

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Paul R. Anderson, Carmen Molina-Paris, Emil Mottola. 2002-04-27. Linear Response and the Validity of the Semi-Classical Approximation in Gravity. https://arxiv.org/abs/gr-qc/0204083

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