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Semiclassical backreaction on asymptotically anti--de Sitter black holes

Taylor, Peter orcid logoORCID: 0000-0002-8416-6408 and Breen, Cormac orcid logoORCID: 0000-0002-1606-8208 (2021) Semiclassical backreaction on asymptotically anti--de Sitter black holes. Physical Review D, 103 (2). ISSN 1550-7998

We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWittSchwinger approximation. The latter approximation must be modified so that it possesses the correct renormalization freedom required to ensure the semiclassical equations are consistent. Equipped with these approximations, the reduced-order field equations are easily integrated and the first-order (in ℏ) corrections to the metric are obtained. We also compute the corrections to the black hole event horizon, surface gravity, and minimum temperature as well as corrections to the photon sphere and quadratic curvature invariants. We pay particular attention to the temperature profiles of the semiclassical black holes compared with their classical counterparts, pointing out some interesting qualitative features produced by the backreaction. These results ought to provide reasonable approximations to the first-order (one-loop) quantum backreaction on the geometry of asymptotically anti–de Sitter black holes when the exact numerical stress-energy tensor sources the semiclassical equations.
Item Type:Article (Published)
Additional Information:Article number: 025006
Mathematics > Differential equations
Mathematics > Mathematical physics
Mathematics > Relativity
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:American Physical Society
Official URL:https://doi.org/10.1103/PhysRevD.103.025006
Copyright Information:© 2021 American Physical Society (APS)
ID Code:27639
Deposited On:13 Apr 2023 15:29 by Peter Taylor . Last Modified 13 Apr 2023 15:29

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