Black holes and nilmanifolds: quasinormal modes as the fingerprints of extra dimensions?

Anna Chrysostomou; Alan Cornell; Aldo Deandrea; Étienne Ligout; Dimitrios Tsimpis

doi:10.1140/epjc/s10052-023-11496-w

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 325
https://doi.org/10.1140/epjc/s10052-023-11496-w

Regular Article - Theoretical Physics

Black holes and nilmanifolds: quasinormal modes as the fingerprints of extra dimensions?

Anna Chrysostomou¹^,2^a, Alan Cornell¹^,2, Aldo Deandrea¹^,2, Étienne Ligout³ and Dimitrios Tsimpis²

¹ Department of Physics, University of Johannesburg, PO Box 524, 2006, Auckland Park, South Africa
² Institut de Physique des Deux Infinis de Lyon, Université de Lyon, UCBL, UMR 5822, CNRS/IN2P3. 4, rue Enrico Fermi, 69622, Villeurbanne Cedex, France
³ École Normale Supérieure de Lyon, BP 7000, 15 parvis René Descartes, 69342, Lyon Cedex 07, France

^a chrysostomou@ip2i.in2p3.fr

Received: 30 December 2022
Accepted: 9 April 2023
Published online: 25 April 2023

Abstract

We investigate whether quasinormal modes (QNMs) can be used in the search for signatures of extra dimensions. To address a gap in the Beyond the Standard Model (BSM) literature, we focus here on higher dimensions characterised by negative Ricci curvature. As a first step, we consider a product space comprised of a four-dimensional Schwarzschild black hole space-time and a three-dimensional nilmanifold (twisted torus); we model the black hole perturbations as a scalar test field. We suggest that the extra-dimensional geometry can be stylised in the QNM effective potential as a squared mass-like term representing the Kaluza–Klein (KK) spectrum. We then compute the corresponding QNM spectrum using three different numerical methods, and determine a possible “detectability bound” beyond which KK masses cannot be detected using QNMs.

© The Author(s) 2023

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