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# Kerr metric

The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical event horizon. [1]

92 relations: Alfred Schild, Angular momentum, Asymptotically flat spacetime, Axial symmetry, Black hole, Boyer–Lindquist coordinates, Brandon Carter, Carter constant, Cartesian coordinate system, Cauchy horizon, Circular symmetry, Closed timelike curve, Colatitude, Constant of motion, Coordinate singularity, Coordinate system, Cosmic censorship hypothesis, Covariance and contravariance of vectors, Differential operator, Dust solution, Eddington–Finkelstein coordinates, Einstein field equations, Electric charge, Epicyclic gearing, Equations of motion, Equivalence principle, Ergosphere, Event horizon, Exact solutions in general relativity, First observation of gravitational waves, Four-gradient, Four-momentum, Frame-dragging, Gamma-ray burst, General relativity, Geodesic, Gravitational plane wave, Gravitational singularity, Gravity Probe B, Hamilton–Jacobi equation, Homotopy, Integrable system, Invariant mass, Karl Schwarzschild, Kerr–Newman metric, Killing horizon, Killing tensor, Killing vector field, Lense–Thirring precession, Mach's principle, ... Expand index (42 more) »

## Alfred Schild

Alfred Schild (September 7, 1921 &ndash; May 24, 1977) was a leading German-American physicist, well known for his contributions to the Golden age of general relativity (1960–1975).

## Angular momentum

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.

## Asymptotically flat spacetime

An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime.

## Axial symmetry

Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.

## Black hole

A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it.

## Boyer–Lindquist coordinates

In the mathematical description of general relativity, the Boyer–Lindquist coordinates are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole.

## Brandon Carter

Brandon Carter, FRS (born 1942) is an Australian theoretical physicist, best known for his work on the properties of black holes and for being the first to name and employ the anthropic principle in its contemporary form.

## Carter constant

The Carter constant is a conserved quantity for motion around black holes in the general relativistic formulation of gravity.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

## Cauchy horizon

In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations).

## Circular symmetry

In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself.

## Closed timelike curve

In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point.

## Colatitude

In spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90° and the latitude, where southern latitudes are denoted with a minus sign.

## Constant of motion

In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion.

## Coordinate singularity

A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame.

## Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

## Cosmic censorship hypothesis

The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity.

## Covariance and contravariance of vectors

In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.

## Differential operator

In mathematics, a differential operator is an operator defined as a function of the differentiation operator.

## Dust solution

In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure.

## Eddington–Finkelstein coordinates

In general relativity, Eddington–Finkelstein coordinates are a pair of coordinate systems for a Schwarzschild geometry (i.e. a spherically symmetric black hole) which are adapted to radial null geodesics.

## Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

## Electric charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

## Epicyclic gearing

An epicyclic gear train (also known as planetary gear) consists of two gears mounted so that the center of one gear revolves around the center of the other.

## Equations of motion

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.

## Equivalence principle

In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

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## Event horizon

In general relativity, an event horizon is a region in spacetime beyond which events cannot affect an outside observer.

## Exact solutions in general relativity

In general relativity, an exact solution is a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field.

## First observation of gravitational waves

The first observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016.

In differential geometry, the four-gradient (or 4-gradient) \mathbf is the four-vector analogue of the gradient \vec from Gibbs–Heaviside vector calculus.

## Four-momentum

In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime.

## Frame-dragging

Frame-dragging is an effect on spacetime, predicted by Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy.

## Gamma-ray burst

In gamma-ray astronomy, gamma-ray bursts (GRBs) are extremely energetic explosions that have been observed in distant galaxies.

## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

## Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

## Gravitational plane wave

In general relativity, a gravitational plane wave is a special class of a vacuum pp-wave spacetime, and may be defined in terms of Brinkmann coordinates by ds^2.

## Gravitational singularity

A gravitational singularity or spacetime singularity is a location in spacetime where the gravitational field of a celestial body becomes infinite in a way that does not depend on the coordinate system.

## Gravity Probe B

Gravity Probe B (GP-B) was a satellite-based mission which launched on 20 April 2004 on a Delta II rocket.

## Hamilton–Jacobi equation

In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation.

## Homotopy

In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.

## Integrable system

In the context of differential equations to integrate an equation means to solve it from initial conditions.

## Invariant mass

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system.

## Karl Schwarzschild

Karl Schwarzschild (October 9, 1873 – May 11, 1916) was a German physicist and astronomer.

## Kerr–Newman metric

The Kerr–Newman metric is a solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding a charged, rotating mass.

## Killing horizon

A Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killing vector field (both are named after Wilhelm Killing).

## Killing tensor

A Killing tensor, named after Wilhelm Killing, is a symmetric tensor, known in the theory of general relativity, K that satisfies where the parentheses on the indices refer to the symmetric part.

## Killing vector field

In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric.

## Lense–Thirring precession

In general relativity, Lense–Thirring precession or the Lense–Thirring effect (named after Josef Lense and Hans Thirring) is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth.

## Mach's principle

In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach.

## Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

## Mass–energy equivalence

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula: E.

## Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

## Momentum

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.

## Multipole expansion

A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere.

## Naked singularity

In general relativity, a naked singularity is a gravitational singularity without an event horizon.

## Neutron star

A neutron star is the collapsed core of a large star which before collapse had a total of between 10 and 29 solar masses.

## Noether's theorem

Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.

## Oblate spheroidal coordinates

Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci.

## Paul Davies

Paul Charles William Davies, AM (born 22 April 1946) is an English physicist, writer and broadcaster, a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science.

## Penrose process

The Penrose process (also called Penrose mechanism) is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole.

## Petrov classification

In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.

## Photon sphere

A photon sphere is a spherical region of space where gravity is strong enough that photons are forced to travel in orbits.

## Poincaré group

The Poincaré group, named after Henri Poincaré (1906), was first defined by Minkowski (1908) as the group of Minkowski spacetime isometries.

## Point source

A point source is a single identifiable localised source of something.

## Proper time

In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line.

## Reissner–Nordström metric

In physics and astronomy, the Reissner&ndash;Nordström metric is a static solution to the Einstein-Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. The metric was discovered by Hans Reissner, Hermann Weyl, Gunnar Nordström and G. B. Jeffery.

## Ring singularity

A ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring.

## Roger Penrose

Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist, mathematician and philosopher of science.

## Rotating black hole

A rotating black hole is a black hole that possesses angular momentum.

## Rotational energy

Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy.

## Roy Kerr

Roy Patrick Kerr (born 16 May 1934) is a New Zealand mathematician who discovered the Kerr geometry, an exact solution to the Einstein field equation of general relativity.

## Schwarzschild coordinates

In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.

## Schwarzschild metric

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a physical parameter that shows up in the Schwarzschild solution to Einstein's field equations, corresponding to the radius defining the event horizon of a Schwarzschild black hole.

## Singularity (mathematics)

In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.

## Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

## Spacetime topology

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity.

## Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

## Spin-flip

A black hole spin-flip occurs when the spin axis of a rotating black hole undergoes a sudden change in orientation due to absorption of a second (smaller) black hole.

## Static spacetime

In general relativity, a spacetime is said to be static if it does not change over time and is also irrotational.

## Static spherically symmetric perfect fluid

In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure.

## Stationary spacetime

In general relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killing vector that is asymptotically timelike.

## Taub–NUT space

The Taub–NUT metric is an exact solution to Einstein's equations.

## Test particle

In physical theories, a test particle is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.

## Thibault Damour

Thibault Damour (born 7 February 1951) is a French physicist.

## Time translation symmetry

Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval.

## Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

## Vacuum solution

A vacuum solution is a solution of a field equation in which the sources of the field are taken to be identically zero.

## Wahlquist fluid

In general relativity, the Wahlquist fluid is an exact rotating perfect fluid solution to Einstein's equation with equation of state corresponding to constant gravitational mass density.

## Weyl tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold.

## World line

The world line (or worldline) of an object is the path that object traces in -dimensional spacetime.

## References

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