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Title: Vacuum polarization in asymptotically anti-de Sitter black hole geometries

Abstract

We study the polarization of the vacuum for a scalar field, <{phi}{sup 2}>, on a asymptotically anti-de Sitter black hole geometry. The method we follow uses the WKB analytic expansion and point-splitting regularization, similar to previous calculations in the asymptotically flat case. Following standard procedures, we write the Green function, regularize the initial divergent expression by point-splitting, renormalize it by subtracting geometrical counterterms, and take the coincidence limit in the end. After explicitly demonstrating the cancellation of the divergences and the regularity of the Green function, we express the result as a sum of two parts. One is calculated analytically and the result is expressed in terms of some generalized zeta functions, which appear in the computation of functional determinants of Laplacians on Riemann spheres. We also describe some systematic methods to evaluate these functions numerically. Interestingly, the WKB approximation naturally organizes <{phi}{sup 2}> as a series in such zeta functions. We demonstrate this explicitly up to next-to-leading order in the WKB expansion. The other term represents the 'remainder' of the WKB approximation and depends on the difference between an exact (numerical) expression and its WKB counterpart. This has to be dealt with by means of numerical approximation. The generalmore » results are specialized to the case of Schwarzschild-anti-de Sitter black hole geometries. The method is efficient enough to solve the semiclassical Einstein's equations taking into account the backreaction from quantum fields on asymptotically anti-de Sitter black holes.« less

Authors:
;  [1]
  1. Yukawa Institute for Theoretical Physics, Kyoto University (Japan)
Publication Date:
OSTI Identifier:
21254092
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 78; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.78.064011; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; CANCELLATION; DE SITTER GROUP; EINSTEIN FIELD EQUATIONS; GREEN FUNCTION; LAPLACIAN; POLARIZATION; QUANTUM FIELD THEORY; RENORMALIZATION; RIEMANN SPACE; SCALAR FIELDS; SEMICLASSICAL APPROXIMATION; VACUUM POLARIZATION; WKB APPROXIMATION

Citation Formats

Flachi, Antonino, Tanaka, Takahiro, and Department of Physics, Kyoto University. Vacuum polarization in asymptotically anti-de Sitter black hole geometries. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.78.064011.
Flachi, Antonino, Tanaka, Takahiro, & Department of Physics, Kyoto University. Vacuum polarization in asymptotically anti-de Sitter black hole geometries. United States. https://doi.org/10.1103/PHYSREVD.78.064011
Flachi, Antonino, Tanaka, Takahiro, and Department of Physics, Kyoto University. 2008. "Vacuum polarization in asymptotically anti-de Sitter black hole geometries". United States. https://doi.org/10.1103/PHYSREVD.78.064011.
@article{osti_21254092,
title = {Vacuum polarization in asymptotically anti-de Sitter black hole geometries},
author = {Flachi, Antonino and Tanaka, Takahiro and Department of Physics, Kyoto University},
abstractNote = {We study the polarization of the vacuum for a scalar field, <{phi}{sup 2}>, on a asymptotically anti-de Sitter black hole geometry. The method we follow uses the WKB analytic expansion and point-splitting regularization, similar to previous calculations in the asymptotically flat case. Following standard procedures, we write the Green function, regularize the initial divergent expression by point-splitting, renormalize it by subtracting geometrical counterterms, and take the coincidence limit in the end. After explicitly demonstrating the cancellation of the divergences and the regularity of the Green function, we express the result as a sum of two parts. One is calculated analytically and the result is expressed in terms of some generalized zeta functions, which appear in the computation of functional determinants of Laplacians on Riemann spheres. We also describe some systematic methods to evaluate these functions numerically. Interestingly, the WKB approximation naturally organizes <{phi}{sup 2}> as a series in such zeta functions. We demonstrate this explicitly up to next-to-leading order in the WKB expansion. The other term represents the 'remainder' of the WKB approximation and depends on the difference between an exact (numerical) expression and its WKB counterpart. This has to be dealt with by means of numerical approximation. The general results are specialized to the case of Schwarzschild-anti-de Sitter black hole geometries. The method is efficient enough to solve the semiclassical Einstein's equations taking into account the backreaction from quantum fields on asymptotically anti-de Sitter black holes.},
doi = {10.1103/PHYSREVD.78.064011},
url = {https://www.osti.gov/biblio/21254092}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 78,
place = {United States},
year = {Mon Sep 15 00:00:00 EDT 2008},
month = {Mon Sep 15 00:00:00 EDT 2008}
}