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arXiv · 2102.00478

Divergent part of the stress-energy tensor for Maxwell's theory in curved space-time: a systematic derivation

Roberto Niardi·Giampiero Esposito·Francesco Tramontano
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Abstract

In this paper the Feynman Green function for Maxwell's theory in curved space-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.

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Roberto Niardi, Giampiero Esposito, Francesco Tramontano. 2021-01-31. Divergent part of the stress-energy tensor for Maxwell's theory in curved space-time: a systematic derivation. https://arxiv.org/abs/2102.00478

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