# 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:

- 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}

}

DOI: 10.21468/SciPostPhys.8.2.017

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