The Kerr Metric

TL;DR

This review covers the discovery, mathematical properties, and astrophysical significance of the Kerr metric, highlighting its role in black hole physics and stability analysis over the past 50 years.

Contribution

It provides a comprehensive overview of the Kerr metric's development, properties, and applications, including new pedagogical derivations and insights into black hole stability.

Findings

Kerr metric describes the most general rotating black hole

Kerr perturbation theory aids in understanding black hole stability

The solution has unique mathematical properties facilitating calculations

Abstract

This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.