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Title: Computing black hole partition functions from quasinormal modes

Abstract

We propose a method of computing one-loop determinants in black hole space-times (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A numerical evaluation must face the fact that the sum over the quasinormal modes, indexed by momentum and overtone numbers, is divergent. A necessary ingredient is then a regularization scheme to handle the divergent contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. Furthermore, we then discuss the application of such techniques to more complicated spacetimes.

Authors:
 [1];  [2];  [3]
  1. Univ. of Virginia, Charlottesville, VA (United States)
  2. Utrecht Univ., Utrecht (The Netherlands)
  3. Univ. of Virginia, Charlottesville, VA (United States); College of William and Mary, Williamsburg, VA (United States)
Publication Date:
Research Org.:
U.S. Dept. of the Navy, Arlington County, VA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1326940
Grant/Contract Number:  
SC0007894
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Black Holes; Holography and condensed matter physics (AdS/CMT); Holography and quark-gluon plasmas

Citation Formats

Arnold, Peter, Szepietowski, Phillip, and Vaman, Diana. Computing black hole partition functions from quasinormal modes. United States: N. p., 2016. Web. doi:10.1007/JHEP07(2016)032.
Arnold, Peter, Szepietowski, Phillip, & Vaman, Diana. Computing black hole partition functions from quasinormal modes. United States. doi:10.1007/JHEP07(2016)032.
Arnold, Peter, Szepietowski, Phillip, and Vaman, Diana. Thu . "Computing black hole partition functions from quasinormal modes". United States. doi:10.1007/JHEP07(2016)032. https://www.osti.gov/servlets/purl/1326940.
@article{osti_1326940,
title = {Computing black hole partition functions from quasinormal modes},
author = {Arnold, Peter and Szepietowski, Phillip and Vaman, Diana},
abstractNote = {We propose a method of computing one-loop determinants in black hole space-times (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A numerical evaluation must face the fact that the sum over the quasinormal modes, indexed by momentum and overtone numbers, is divergent. A necessary ingredient is then a regularization scheme to handle the divergent contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. Furthermore, we then discuss the application of such techniques to more complicated spacetimes.},
doi = {10.1007/JHEP07(2016)032},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2016,
place = {United States},
year = {Thu Jul 07 00:00:00 EDT 2016},
month = {Thu Jul 07 00:00:00 EDT 2016}
}

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Cited by: 2 works
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