Computing black hole partition functions from quasinormal modes
Abstract
We propose a method of computing oneloop determinants in black hole spacetimes (with emphasis on asymptotically antide Sitter black holes) that may be used for numerics when completelyanalytic results are unattainable. The method utilizes the expression for oneloop 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 fixedmomentum sectors to the partition function. To this end, we formulate an effective twodimensional 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 oneloop determinant in the BTZ black hole background. Furthermore, 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)
 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 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdSCFT Correspondence; Black Holes; Holography and condensed matter physics (AdS/CMT); Holography and quarkgluon 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. 2016.
"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 oneloop determinants in black hole spacetimes (with emphasis on asymptotically antide Sitter black holes) that may be used for numerics when completelyanalytic results are unattainable. The method utilizes the expression for oneloop 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 fixedmomentum sectors to the partition function. To this end, we formulate an effective twodimensional 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 oneloop 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 = 2016,
month = 7
}

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