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 (52)

• A Massive Pulsar in a Compact Relativistic Binary
• Quasinormal modes of black holes and black branes
• Quasinormal modes of black holes: from astrophysics to string theory
• A rotating black ring in five dimensions
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• The Thermodynamics of Black Holes
• Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes
• The motion of point particles in curved spacetime
• The Black Hole Mass Distribution in the Galaxy
• Black Holes in Higher Dimensions
• Broad iron lines in Active Galactic Nuclei
• Stationary Black Holes: Uniqueness and Beyond
• Hawking Radiation and Black Hole Thermodynamics
• Measuring Black Hole Spin using X-ray Reflection Spectroscopy
• Analytic black hole perturbation approach to gravitational radiation
• Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets
• On the gravitational field of a mass point according to Einstein's theory
• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Black Saturn
• Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions
• Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*
• Mass Measurements of Stellar and Intermediate Mass Black-Holes
• The old nuclear star cluster in the Milky Way: dynamics, mass, statistical parallax, and black hole mass
• The Spin of Supermassive Black Holes
• Spacetime approach to force-free magnetospheres
• 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
• Classes of Exact Solutions to the Teukolsky Master Equation
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Analytic Solutions of the Teukolsky Equation and their Properties
• Extracting black-hole rotational energy: The generalized Penrose process
• New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation
• Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime
• Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes
• Blandford-Znajek mechanism versus Penrose process
• On the Maximum Mass of Neutron Stars
• Testing the black hole no-hair theorem at the galactic center: Perturbing effects of stars in the surrounding cluster
• Teukolsky-Starobinsky Identities - a Novel Derivation and Generalizations
• Momentum flow in black-hole binaries: II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins
• Electromotive Force in the Blandford-Znajek Process
• The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis
• Algebraic Classification of Numerical Spacetimes and Black-Hole-Binary Remnants
• Observational Evidence for Black Holes
• Discovering the Kerr and Kerr-Schild metrics
• Causal extraction of black hole rotational energy by various kinds of electromagnetic fields
• Degeneracy measures for the algebraic classification of numerical spacetimes
• A novel derivation of the rotating black hole metric
• Black holes and thermodynamics - The first half century
• Numerical investigation of black hole interiors
• Gravitational field of a Schwarzschild black hole and a rotating mass ring
• De/re-constructing the Kerr Metric
• Race for the Kerr field

Cited by in corpus (110)

• Testing General Relativity with Present and Future Astrophysical Observations
• Black holes, hidden symmetries, and complete integrability
• Nonlinearities in Black Hole Ringdowns
• Numerical Methods for Finding Stationary Gravitational Solutions
• Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
• Directed searches for gravitational waves from ultralight bosons
• Axionic instabilities and new black hole solutions
• The Science of the Einstein Telescope
• On choosing the start time of binary black hole ringdown
• A Modern Approach to Superradiance
• Shadow and quasinormal modes of the Kerr-Newman-Kiselev-Letelier black hole
• Lepton Flavorful Fifth Force and Depth-dependent Neutrino Matter Interactions
• Test black holes, scattering amplitudes and perturbations of Kerr spacetime
• General theories of linear gravitational perturbations to a Schwarzschild Black Hole
• Stability for linearized gravity on the Kerr spacetime
• Multiband gravitational-wave searches for ultralight bosons
• Effective Field Theory for the Perturbations of a Slowly Rotating Black Hole
• Zero mass limit of Kerr spacetime is a wormhole
• Importance of tidal resonances in extreme-mass-ratio inspirals
• Spectral method for metric perturbations of black holes: Kerr background case in general relativity
• Cosmic Censorship and parametrized spinning black-hole geometries
• Angular emission patterns of remnant black holes
• Difficulties of Quantitative Tests of the Kerr-Hypothesis with X-Ray Observations of Mass Accreting Black Holes
• The Kerr-Newman metric: A Review
• Production of Primordial Black Holes via Single Field Inflation and Observational Constraints
• Exploring Axial Symmetry in Modified Teleparallel Gravity
• Are Black Holes Springy?
• Analyzing black-hole ringdowns
• An exact solution for a rotating black hole in modified gravity
• Primordial Black Holes from Axion Domain Wall Collapse
• The massive Dirac equation in the Kerr-Newman-de Sitter and Kerr-Newman black hole spacetimes
• Kerr-(Anti-)de Sitter Black Holes: Perturbations and quasi-normal modes in the slow rotation limit
• Flexible mapping of ringdown amplitudes for nonprecessing binary black holes
• Modes of the Kerr geometry with purely imaginary frequencies
• Deformation of extremal black holes from stringy interactions
• The gravitational capture of compact objects by massive black holes
• Analyzing black-hole ringdowns II: data conditioning
• Killing horizons and surface gravities for a well-behaved three-function generalisation of the Kerr spacetime
• Ringdown mode amplitudes of precessing binary black holes
• Infinitely degenerate exact Ricci-flat solutions in f(R) gravity
• Identifying modified theories of gravity using binary black-hole ringdowns
• A local non-negative initial data scalar characterisation of the Kerr solution
• A spectral method algorithm for numerical simulations of gravitational fields
• Separating metric perturbations in near-horizon extremal Kerr
• Is there a mode stability paradox for neutrino perturbations of Kerr black holes?
• Simulation-based inference of black hole ringdowns in the time domain
• Energy Extraction From Non-Coalescing Black Hole Binaries
• Towards a Gordon form of the Kerr spacetime
• Physically motivated ansatz for the Kerr spacetime
• The imprint of superradiance on hierarchical black hole mergers
• A Black-Hole Primer: Particles, Waves, Critical Phenomena and Superradiant Instabilities
• The Teukolsky--Starobinsky constants: facts and fictions
• The Lense-Thirring effect on the Galilean moons of Jupiter
• Compact Objects in Alternative Gravities
• Painleve-Gullstrand coordinates versus Kerr spacetime geometry
• Electromagnetic signatures of strong-field gravity from accreting black holes
• Limitations in Testing the Lense-Thirring Effect with LAGEOS and the Newly Launched Geodetic Satellite LARES 2
• Consistent derivation of the Hawking effect for both non-extremal and extremal Kerr black holes
• The Effect of Spacetime Curvature on Statistical Distributions
• Probing Particle Physics with Gravitational Waves
• Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle
• Cumulative effect of orbital resonances in extreme-mass-ratio inspirals
• Optimizing Neural Network Surrogate Models: Application to Black Hole Merger Remnants
• Energy extraction in electrostatic extreme binary black holes
• Acceleration of charged particles from near-extremal rotating black holes embedded in magnetic fields
• Stealth Chaos due to Frame Dragging
• Hawking effect in an extremal Kerr black hole spacetime
• Hawking radiation in multi-horizon spacetimes using Hamilton Jacobi method
• Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
• Exotic compact object behavior in black hole analogues
• The Lense-Thirring effect at work in M87${}^{\ast }$
• Strong Gravitational Lensing Effects of the Rotating Short-Haired Black Hole and Constraints from EHT Observations
• Parametric-resonance based phenomenology of gravitating axion configurations
• Elliptic boundary value problems for the stationary vacuum spacetimes
• Wave equations in conformally separable, accreting, rotating black holes
• Post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an axisymmetric body
• Numerical Relativity and the Discovery of Gravitational Waves
• On Some Applications of the Sagnac Effect
• Can a radiation gauge be horizon-locking?
• Kerr black hole in the formalism of isolated horizons
• Point particles and Appell's solutions on the axis of Kerr black hole for arbitrary spin in terms of the Debye potentials
• The Effect of Stationary Axisymmetric Spacetimes in Interferometric Visibility
• Chaotic Dynamics in Extremal Black Holes: A Challenge to the Chaos Bound
• Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region
• Evolution of Braneworld Kerr-Newman Naked Singularities
• Invariant Renormalization-Group improvement
• Acoustic Analogues of Extremal Rotating Black Holes in Exciton-Polariton Condensates
• Determination of the angular momentum of the Kerr black hole from equatorial geodesic motion
• Matter environments around black holes: geodesics, light rings, and ultracompact configurations
• Thermal radiation in curved spacetime using influence functional formalism
• Quasinormal mode frequencies of Kerr black holes from Regge trajectories
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores
• On the Euler-type gravitomagnetic orbital effects in the field of a precessing body
• Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy
• The no-hair theorems at work in M87${}^{\ast }$
• Black-hole ringdown with templates capturing spin precession: A reanalysis of GW190521
• Motion equations in a Kerr-Newman-de Sitter spacetime: some methods of integration and application to black holes shadowing in Scilab
• A 4D asymptotically flat rotating black hole solution including supertraslation correction
• On a Class of Exact Arbitrarily Differentiable de Sitter Cores with Kerr Exteriors: Possible gravastar or regular black hole mimickers
• Review of the Gravitomagnetic Clock Effect
• A spectral approach to numerical simulations of the ADM equations
• Observational assessment of the viability of de Sitter-Gödel-de Sitter phase transition
• Zero Mass limit of Kerr-MOG Black Hole Equals Wormhole
• Generalized spheroidal wave equation for real and complex valued parameters. An algorithm based on the analytic derivatives for the eigenvalues
• Macroscopic approaches to rotating neutron stars
• The no-hair theorems at work in the tidal disruption event AT2020afhd
• Constraining Kerr supermassive black hole properties using gravitational waves from inspiraling stellar-mass binary black holes
• Nethotrons: exploring the possibility of measuring relativistic spin precessions, from Earth's satellites to the Galactic Centre
• Alternative characterization of a black hole boundary
• Wavy way to the Kerr metric and the quantum nature of its ring singularity