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

TL;DR

This paper explores how quasinormal modes of black holes in higher-dimensional spaces with nilmanifolds could reveal signatures of extra dimensions, providing a potential observational tool for beyond Standard Model physics.

Contribution

It introduces a novel approach to detect extra dimensions via QNM spectra in a specific higher-dimensional black hole model with nilmanifolds.

Findings

Computed QNM spectra using three numerical methods.

Identified a detectability bound for Kaluza-Klein masses.

Proposed QNMs as potential signatures of extra dimensions.

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.