Reissner–Nordström metric

E14555

Lorentzian metric black hole metric electrovacuum solution exact solution of Einstein field equations spherically symmetric spacetime static spacetime

The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.

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All labels observed (5)

Label	Occurrences
Reissner–Nordström black hole	5
Reissner–Nordström metric canonical	4
Reissner–Nordström spacetime	3
Reissner–Nordström solution	2
Reissner–Nordström radius for charged black holes	1

How this entity was disambiguated

This entity first appeared as the object of triple T79914 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Reissner–Nordström metric
Context triple: [Einstein field equations, admitsSolution, Reissner–Nordström metric]

A. Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
B. Schwarzschild black hole
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.
C. Eddington–Finkelstein coordinates
Eddington–Finkelstein coordinates are a coordinate system in general relativity that smoothly covers a black hole’s event horizon, avoiding the coordinate singularity present in standard Schwarzschild coordinates.
D. Kruskal–Szekeres coordinates
Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.
E. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Reissner–Nordström metric
Target entity description: The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.

A. Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
B. Schwarzschild black hole
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.
C. Eddington–Finkelstein coordinates
Eddington–Finkelstein coordinates are a coordinate system in general relativity that smoothly covers a black hole’s event horizon, avoiding the coordinate singularity present in standard Schwarzschild coordinates.
D. Kruskal–Szekeres coordinates
Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.
E. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
F. None of above. chosen

Statements (47)

Predicate	Object
instanceOf	Lorentzian metric ⓘ black hole metric ⓘ electrovacuum solution ⓘ exact solution of Einstein field equations ⓘ spherically symmetric spacetime ⓘ static spacetime ⓘ
associatedElectromagneticPotential	A_\mu dx^\mu = -\frac{Q}{r} dt ⓘ
BekensteinHawkingEntropy	S = \frac{A_+}{4} with A_+ = 4\pi r_+^2 ⓘ
belongsToTheory	general relativity ⓘ
canBeExtendedBy	Eddington–Finkelstein coordinates ⓘ Kruskal-like coordinates ⓘ
dependsOnParameter	electric charge parameter Q ⓘ mass parameter M ⓘ
describes	electrically charged black hole ⓘ spacetime geometry outside a static spherically symmetric electrically charged mass ⓘ
energyMomentumSource	electromagnetic field of a point charge ⓘ
generalizes	Schwarzschild solution to include electric charge ⓘ
hasCauchyHorizon	at r = r_- for \|Q\| < M ⓘ
hasCausalStructure	with multiple asymptotic regions in maximal analytic extension ⓘ
hasCoordinateSingularity	at r = r_+ in Schwarzschild-like coordinates ⓘ
hasCoordinateSystem	Schwarzschild-like coordinates ⓘ linked to: Schwarzschild coordinates
hasCurvatureSingularity	at r = 0 ⓘ
hasEventHorizon	at r = r_+ for \|Q\| \le M ⓘ
hasInnerHorizonRadius	r_- = M - \sqrt{M^2 - Q^2} ⓘ
hasIsometryGroup	R × SO(3) ⓘ
hasKillingVectorField	\partial_t ⓘ generators of SO(3) rotations ⓘ
hasNakedSingularityWhen	\|Q\| > M ⓘ
hasOuterHorizonRadius	r_+ = M + \sqrt{M^2 - Q^2} ⓘ
hasSymmetry	spherical symmetry ⓘ time-translation symmetry ⓘ
HawkingTemperature	T_H = \frac{\kappa_+}{2\pi} ⓘ
HawkingTemperatureExtremal	T_H = 0 for \|Q\| = M ⓘ
isAsymptotically	flat ⓘ
isExtremalWhen	\|Q\| = M ⓘ
isSolutionType	static spherically symmetric electrovacuum solution ⓘ
isUsedIn	analyses of cosmic censorship conjecture ⓘ studies of charged black hole thermodynamics ⓘ studies of inner horizon instability ⓘ
lineElement	ds^2 = -\left(1 - \frac{2M}{r} + \frac{Q^2}{r^2}\right) dt^2 + \left(1 - \frac{2M}{r} + \frac{Q^2}{r^2}\right)^{-1} dr^2 + r^2 d\Omega^2 ⓘ
namedAfter	Gunnar Nordström ⓘ Hans Reissner ⓘ
obeys	Birkhoff-like theorem for charged spherically symmetric solutions ⓘ
reducesTo	Schwarzschild metric when Q = 0 ⓘ
satisfies	vacuum Einstein equations with electromagnetic stress-energy tensor ⓘ
solves	Einstein–Maxwell equations ⓘ
surfaceGravityAtOuterHorizon	\kappa_+ = \frac{\sqrt{M^2 - Q^2}}{r_+^2} ⓘ

How these facts were elicited