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Title: Connecting quasinormal modes and heat kernels in 1-loop determinants

Abstract

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

Authors:
 [1];  [1];  [1]
  1. Arizona State University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1596878
Grant/Contract Number:  
SC0018330
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 8 Journal Issue: 2; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Keeler, Cynthia, Martin, Victoria, and Svesko, Andrew. Connecting quasinormal modes and heat kernels in 1-loop determinants. Netherlands: N. p., 2020. Web. doi:10.21468/SciPostPhys.8.2.017.
Keeler, Cynthia, Martin, Victoria, & Svesko, Andrew. Connecting quasinormal modes and heat kernels in 1-loop determinants. Netherlands. doi:10.21468/SciPostPhys.8.2.017.
Keeler, Cynthia, Martin, Victoria, and Svesko, Andrew. Mon . "Connecting quasinormal modes and heat kernels in 1-loop determinants". Netherlands. doi:10.21468/SciPostPhys.8.2.017.
@article{osti_1596878,
title = {Connecting quasinormal modes and heat kernels in 1-loop determinants},
author = {Keeler, Cynthia and Martin, Victoria and Svesko, Andrew},
abstractNote = {We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.},
doi = {10.21468/SciPostPhys.8.2.017},
journal = {SciPost Physics Proceedings},
number = 2,
volume = 8,
place = {Netherlands},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.8.2.017

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