Kerr metric

E14416

Lorentzian metric black hole solution exact solution of Einstein field equations stationary axisymmetric spacetime vacuum solution in general relativity

The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.

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Observed surface forms (4)

Surface form	Occurrences
Kerr black hole	5
Kerr spacetime	5
Kerr solution	1
Lense–Thirring precession	1

Statements (48)

Predicate	Object
instanceOf	Lorentzian metric ⓘ black hole solution ⓘ exact solution of Einstein field equations ⓘ stationary axisymmetric spacetime ⓘ vacuum solution in general relativity ⓘ
allows	Penrose process for energy extraction ⓘ superradiant scattering ⓘ
appliesTo	rotating uncharged black holes ⓘ
belongsToTheory	general relativity ⓘ
describes	exterior gravitational field of a rotating mass ⓘ spacetime geometry around a rotating uncharged black hole ⓘ
dimension	4-dimensional spacetime ⓘ
generalizes	Schwarzschild black hole ⓘ surface form: Schwarzschild solution
hasCondition	\|a\| ≤ M for a black hole ⓘ
hasCoordinateSystem	Boyer–Lindquist coordinates ⓘ Kerr–Schild coordinates ⓘ
hasCurvatureInvariant	nonzero Kretschmann scalar ⓘ
hasEffect	Lense–Thirring precession near the black hole ⓘ
hasFeature	Killing horizon ⓘ ergosphere ⓘ event horizon ⓘ frame dragging ⓘ ring singularity ⓘ
hasInvariant	Kerr parameter a = J/M ⓘ
hasParameter	mass parameter M ⓘ spin parameter a ⓘ
hasProperty	Ricci-flat ⓘ asymptotically flat ⓘ axisymmetric ⓘ stationary ⓘ vacuum ⓘ
hasRegion	ergosphere between event horizon and static limit ⓘ inner Cauchy horizon at r_- = M - sqrt(M^2 - a^2) ⓘ outer event horizon at r_+ = M + sqrt(M^2 - a^2) ⓘ
hasSymmetry	axial symmetry ⓘ time-translation symmetry ⓘ two commuting Killing vector fields ⓘ
hasTopology	ring-shaped singularity in the equatorial plane ⓘ
isGeneralizedBy	Kerr–Newman black hole ⓘ surface form: Kerr–Newman metric
isUsedIn	accretion disk models around black holes ⓘ astrophysical modeling of rotating black holes ⓘ gravitational wave modeling from compact binaries ⓘ
reducesTo	Schwarzschild metric when spin parameter a = 0 ⓘ
satisfies	vacuum Einstein equations R_{μν} = 0 ⓘ
signature	Lorentzian signature (-,+,+,+) ⓘ
solves	Einstein field equations in vacuum ⓘ
wasProposedBy	Roy Kerr ⓘ
yearProposed	1963 ⓘ

Referenced by (20)

Full triples — surface form annotated when it differs from this entity's canonical label.

Einstein field equations → admitsSolution → Kerr metric ⓘ

Penrose process for energy extraction → appliesTo → Kerr metric ⓘ

this entity surface form: Kerr black hole

Penrose–Carter diagrams → appliesTo → Kerr metric ⓘ

subject surface form: Penrose–Carter diagram

this entity surface form: Kerr spacetime

Kerr Penrose diagram → basedOn → Kerr metric ⓘ

Israel–Carter–Robinson uniqueness theorems → concerns → Kerr metric ⓘ

this entity surface form: Kerr black hole

The Mathematical Theory of Black Holes → covers → Kerr metric ⓘ

Penrose process for energy extraction → describedIn → Kerr metric ⓘ

Kerr–Newman black hole → generalizes → Kerr metric ⓘ

this entity surface form: Kerr black hole

Kerr–Newman black hole → hasEffect → Kerr metric ⓘ

this entity surface form: Lense–Thirring precession

general relativity → includes → Kerr metric ⓘ

Boyer–Lindquist coordinates → introducedInContext → Kerr metric ⓘ

this entity surface form: Kerr solution

Roy Kerr → knownFor → Kerr metric ⓘ

The Mathematical Theory of Black Holes → mainSubject → Kerr metric ⓘ

this entity surface form: Kerr black hole

Penrose process for energy extraction → mathematicalFramework → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Roy Kerr → notableConcept → Kerr metric ⓘ

this entity surface form: Kerr black hole

Roy Kerr → notableConcept → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Kerr–Schild coordinates → relatedTo → Kerr metric ⓘ

Kerr Penrose diagram → represents → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Boyer–Lindquist coordinates → usedFor → Kerr metric ⓘ

Kerr–Schild coordinates → usedIn → Kerr metric ⓘ

this entity surface form: Kerr spacetime