Schwarzschild black hole

E1310

astrophysical object model black hole solution exact solution of Einstein field equations

A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.

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Observed surface forms (13)

Surface form	Occurrences
Schwarzschild metric	17
Schwarzschild solution	7
Schwarzschild spacetime	4
Schwarzschild solution to Einstein field equations	2
Kerr black hole with zero spin	1
Schwarzschild black hole concept	1
Schwarzschild black hole when charge and angular momentum are zero	1
Schwarzschild exterior	1
Schwarzschild geometry	1
Schwarzschild interior	1
Schwarzschild line element	1
Schwarzschild manifold	1
Schwarzschild metric derivation	1

Statements (49)

Predicate	Object
instanceOf	astrophysical object model ⓘ black hole solution ⓘ exact solution of Einstein field equations ⓘ
alternativeCoordinates	Eddington–Finkelstein coordinates ⓘ Kruskal–Szekeres coordinates ⓘ
approximates	non-rotating astrophysical black hole ⓘ
belongsToClass	asymptotically flat spacetimes ⓘ stationary black holes ⓘ
coordinateSystemUsed	Schwarzschild coordinates ⓘ
describedByTheory	theory of relativity ⓘ surface form: general relativity
hasCausalStructure	Kruskal–Szekeres coordinates ⓘ surface form: maximally extended Kruskal–Szekeres spacetime
hasCoordinateSingularity	at r = r_s in Schwarzschild coordinates ⓘ
hasCurvatureDivergence	singularity at r = 0 ⓘ
hasCurvatureInvariant	Kretschmann scalar ⓘ
hasEntropyFormula	Bekenstein–Hawking entropy ⓘ
hasEventHorizon	Schwarzschild radius ⓘ
hasGeodesics	circular photon orbits ⓘ radial timelike geodesics ⓘ
hasGlobalStructureFeature	event horizon separating causally disconnected regions ⓘ
hasHorizonType	non-rotating event horizon ⓘ
hasInnermostStableCircularOrbit	radius 6GM/c^2 for test particles ⓘ
hasLineElement	Schwarzschild black hole self-linksurface differs ⓘ surface form: Schwarzschild line element
hasMetric	Schwarzschild black hole self-linksurface differs ⓘ surface form: Schwarzschild metric
hasParameter	mass ⓘ
hasPenroseDiagram	Schwarzschild Penrose diagram ⓘ
hasPhotonSphere	radius 3GM/c^2 ⓘ
hasProperty	non-rotating ⓘ static ⓘ uncharged ⓘ
hasSchwarzschildRadiusFormula	r_s = 2GM/c^2 ⓘ
hasSingularityType	central curvature singularity ⓘ
hasSpacetimeRegion	Schwarzschild black hole self-linksurface differs ⓘ surface form: Schwarzschild exterior Schwarzschild black hole self-linksurface differs ⓘ surface form: Schwarzschild interior event horizon ⓘ
hasSurfaceGravity	constant over horizon ⓘ
hasSymmetry	spherical symmetry ⓘ
hasTemperature	Hawking temperature ⓘ
isSpecialCaseOf	Schwarzschild black hole self-linksurface differs ⓘ surface form: Kerr black hole with zero spin Reissner–Nordström black hole with zero charge ⓘ
lacksParameter	angular momentum ⓘ electric charge ⓘ
namedAfter	Karl Schwarzschild ⓘ
obeysLaw	black hole area theorem ⓘ black hole no-hair theorem ⓘ
satisfiesEquation	Einstein field equations in vacuum ⓘ
solutionType	vacuum solution ⓘ
usedIn	accretion disk models ⓘ gravitational lensing calculations ⓘ tests of general relativity ⓘ

Referenced by (48)

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

Einstein field equations → admitsSolution → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Schwarzschild radius → appearsIn → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild solution to Einstein field equations

Kruskal–Szekeres coordinates → appliesTo → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Painlevé–Gullstrand coordinates → appliesTo → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild spacetime

Painlevé–Gullstrand coordinates → appliesTo → Schwarzschild black hole ⓘ

Penrose–Carter diagrams → appliesTo → Schwarzschild black hole ⓘ

subject surface form: Penrose–Carter diagram

this entity surface form: Schwarzschild spacetime

Schwarzschild coordinates → associatedWith → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild solution

Schwarzschild radius → associatedWith → Schwarzschild black hole ⓘ

Schwarzschild Penrose diagram → basedOn → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Einstein–Rosen bridge → basedOnSolutionOf → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

"Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie" → citedFor → Schwarzschild black hole ⓘ

subject surface form: Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

this entity surface form: Schwarzschild metric derivation

Israel–Carter–Robinson uniqueness theorems → concerns → Schwarzschild black hole ⓘ

The Mathematical Theory of Black Holes → covers → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Eddington–Finkelstein coordinates → definedOn → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild spacetime

Schwarzschild → describedBy → Schwarzschild black hole ⓘ

subject surface form: Schwarzschild black hole

this entity surface form: Schwarzschild metric

Schwarzschild Penrose diagram → describes → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild spacetime

Schwarzschild coordinates → describes → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

"Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie" → foundationFor → Schwarzschild black hole ⓘ

subject surface form: Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

this entity surface form: Schwarzschild black hole concept

Kerr metric → generalizes → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild solution

Karl → hasConceptNamedAfter → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

Karl → hasConceptNamedAfter → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild metric

Karl → hasConceptNamedAfter → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild solution

Karl Schwarzschild → hasEponym → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Karl Schwarzschild → hasEponym → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild solution

Schwarzschild black hole → hasLineElement → Schwarzschild black hole self-linksurface differs ⓘ

this entity surface form: Schwarzschild line element

Schwarzschild black hole → hasMetric → Schwarzschild black hole self-linksurface differs ⓘ

this entity surface form: Schwarzschild metric

Schwarzschild → hasNameInTheory → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild solution

Schwarzschild → hasNameInTheory → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild geometry

Schwarzschild → hasNameInTheory → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

Schwarzschild black hole → hasSpacetimeRegion → Schwarzschild black hole self-linksurface differs ⓘ

this entity surface form: Schwarzschild interior

Schwarzschild black hole → hasSpacetimeRegion → Schwarzschild black hole self-linksurface differs ⓘ

this entity surface form: Schwarzschild exterior

general relativity → includes → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild solution

"Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie" → introduces → Schwarzschild black hole ⓘ

subject surface form: Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

this entity surface form: Schwarzschild metric

Schwarzschild black hole → isSpecialCaseOf → Schwarzschild black hole self-linksurface differs ⓘ

this entity surface form: Kerr black hole with zero spin

Karl Schwarzschild → knownFor → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Schwarzschild → knownFor → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild metric

Schwarzschild → knownFor → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

Schwarzschild coordinates → mathematicallyDefinedOn → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild manifold

Karl → notableWork → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild metric

Karl → notableWork → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

Karl → notableWork → Schwarzschild black hole ⓘ

subject surface form: Karl Schwarzschild

this entity surface form: Schwarzschild solution to Einstein field equations

Kerr–Newman black hole → reducesTo → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild black hole when charge and angular momentum are zero

Oppenheimer–Snyder model → relatedTo → Schwarzschild black hole ⓘ

Schwarzschild radius → relatedTo → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

"Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie" → topic → Schwarzschild black hole ⓘ

subject surface form: Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

this entity surface form: Schwarzschild solution

Oppenheimer–Snyder model → usesMetric → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric

Kretschmann scalar → valueFor → Schwarzschild black hole ⓘ

this entity surface form: Schwarzschild metric