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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All labels observed (7)

Label	Occurrences
Kerr metric canonical	10
Kerr black hole	7
Kerr spacetime	6
Kerr black holes	2
Kerr solution	1
Kerr solution of Einstein's field equations	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 (28)

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

Einstein field equations → admitsSolution → Kerr metric ⓘ

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

this entity surface form: Kerr black hole

The Mathematical Theory of Black Holes → covers → 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

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

this entity surface form: Kerr black hole

general relativity → includes → Kerr metric ⓘ

Kerr Penrose diagram → represents → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Kerr Penrose diagram → basedOn → Kerr metric ⓘ

Boyer–Lindquist coordinates → usedFor → Kerr metric ⓘ

Boyer–Lindquist coordinates → introducedInContext → Kerr metric ⓘ

this entity surface form: Kerr solution

Penrose process for energy extraction → appliesTo → Kerr metric ⓘ

this entity surface form: Kerr black hole

Penrose process for energy extraction → describedIn → Kerr metric ⓘ

Penrose process for energy extraction → mathematicalFramework → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Kerr–Schild coordinates → usedIn → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Kerr–Schild coordinates → relatedTo → Kerr metric ⓘ

Roy Kerr → knownFor → Kerr metric ⓘ

Roy Kerr → notableConcept → Kerr metric ⓘ

this entity surface form: Kerr black hole

Roy Kerr → notableConcept → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Penrose–Carter diagrams → appliesTo → Kerr metric ⓘ

subject surface form: Penrose–Carter diagram

this entity surface form: Kerr spacetime

Gravitation (with Charles Misner and Kip Thorne) → covers → Kerr metric ⓘ

this entity surface form: Kerr black holes

“Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation” → mainSubject → Kerr metric ⓘ

subject surface form: Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation

this entity surface form: Kerr black hole

“Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation” → usesSpacetimeMetric → Kerr metric ⓘ

subject surface form: Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation

“Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation” → context → Kerr metric ⓘ

subject surface form: Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation

this entity surface form: Kerr solution of Einstein's field equations

Cauchy horizon → occursIn → Kerr metric ⓘ

this entity surface form: Kerr spacetime

Blandford–Znajek process → appliesTo → Kerr metric ⓘ

this entity surface form: Kerr black holes

Richard W. Lindquist → associatedWithConcept → Kerr metric ⓘ

this entity surface form: Kerr black hole

Richard W. Lindquist → appliesTo → Kerr metric ⓘ

subject surface form: Boyer–Lindquist coordinates