The Kerr Metric

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.

37 pages. Submitted to Classical and Quantum Gravity for its "Milestones of General Relativity" focus issue to be published during the Centenary Year of GR. Minor edits to match journal article

References in corpus (13)

• A Massive Pulsar in a Compact Relativistic Binary
• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*
• The old nuclear star cluster in the Milky Way: dynamics, mass, statistical parallax, and black hole mass
• Black ring with two angular momenta
• Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Electromotive Force in the Blandford-Znajek Process
• Discovering the Kerr and Kerr-Schild metrics
• Causal extraction of black hole rotational energy by various kinds of electromagnetic fields
• De/re-constructing the Kerr Metric
• Gravitational field of a Schwarzschild black hole and a rotating mass ring
• Race for the Kerr field

Cited by in corpus (8)

• Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
• Zero mass limit of Kerr spacetime is a wormhole
• Are Black Holes Springy?
• Modes of the Kerr geometry with purely imaginary frequencies
• Separating metric perturbations in near-horizon extremal Kerr
• A Black-Hole Primer: Particles, Waves, Critical Phenomena and Superradiant Instabilities
• Exotic compact object behavior in black hole analogues
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores