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.

Aliases (4)

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 coordinates → surface form: "Schwarzschild-like 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} →

Referenced by (13)

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

Einstein field equations → admitsSolution → Reissner–Nordström metric →

Penrose–Carter diagrams → appliesTo → Reissner–Nordström metric →

subject surface form: "Penrose–Carter diagram"

this entity surface form: "Reissner–Nordström spacetime"

Israel–Carter–Robinson uniqueness theorems → concerns → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström black hole"

Schwarzschild radius → contrastsWith → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström radius for charged black holes"

The Mathematical Theory of Black Holes → covers → Reissner–Nordström metric →

Reissner–Nordström Penrose diagram → describes → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström spacetime"

Kerr–Newman black hole → generalizes → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström black hole"

general relativity → includes → Reissner–Nordström metric →

The Mathematical Theory of Black Holes → mainSubject → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström black hole"

Hans Reissner → notableConcept → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström black hole"

Hans Reissner → notableWork → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström solution"

Einstein–Maxwell equations → usedFor → Reissner–Nordström metric →

this entity surface form: "Reissner–Nordström solution"