Quasi-Normal Modes of Stars and Black Holes

TL;DR

This review discusses the theory and computation of quasi-normal modes of black holes and stars, highlighting their importance in gravitational wave astronomy and summarizing recent advances and limitations in perturbation methods.

Contribution

It provides a comprehensive overview of the mathematical and astrophysical aspects of quasi-normal modes, including perturbations of various black hole types and stars, and reviews numerical techniques used for their calculation.

Findings

Descriptions of different families of quasi-normal modes.

Review of numerical methods for mode calculation.

Discussion of perturbation theory's successes and limitations.

Abstract

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.