Computing black hole partition functions from quasinormal modes
Abstract
We propose a method of computing one-loop determinants in black hole spacetimes (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 \cite{Denef:2009kn}. 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. We then discuss the application of such techniques to more complicated spacetimes.
- Authors:
-
- Univ. of Virginia, Charlottesville, VA (United States)
- Utrecht Univ., Utrecht (The Netherlands)
- 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); Univ. of Virginia, Charlottesville, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1326940
- Alternate Identifier(s):
- OSTI ID: 1774067
- Grant/Contract Number:
- SC0007984
- Resource Type:
- 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. https://doi.org/10.1007/JHEP07(2016)032
Arnold, Peter, Szepietowski, Phillip, and Vaman, Diana. Thu .
"Computing black hole partition functions from quasinormal modes". United States. https://doi.org/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 spacetimes (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 \cite{Denef:2009kn}. 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. 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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