Testing General Relativity with Black Hole Quasi-Normal Modes

TL;DR

This paper reviews how black hole quasi-normal modes can be used to test general relativity, discussing theoretical methods, potential deviations, and recent experimental results from gravitational wave observatories.

Contribution

It provides a comprehensive overview of quasi-normal mode computation methods, deviations from general relativity, and the current experimental status, including detailed tables for advanced readers.

Findings

Comparison of methods to compute quasi-normal modes

Discussion of deviations from general relativity

Review of gravitational wave observational results

Abstract

The purpose of this chapter is to provide an overview of the exciting field of black hole quasi-normal modes and its capabilities to test general relativity in the 21st century. After motivating this line of research, we provide a qualitative introduction to the concept of quasi-normal modes and outline black hole perturbation theory. With the perturbation equations at hand, we discuss common methods to compute the quasi-normal mode spectrum and compare the advantages and disadvantages of each approach. We also provide an overview of possible deviations from general relativity and how they modify the quasi-normal mode spectrum of black holes from a theoretical point of view. We then review the rapidly evolving status of currently operating gravitational wave observatories and experimental results. The chapter concludes with a discussion of open problems and promising outlooks to theoretical and experimental developments. Central pieces that make this chapter particularly interesting, also for advanced readers, are comprehensive tables providing a detailed overview of the status of techniques to compute quasi-normal modes and methods to describe quasi-normal modes of rotating black holes beyond general relativity.