Einstein–Maxwell equations

E78014

equations of motion field equations system of partial differential equations theory in theoretical physics

The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.

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All labels observed (3)

Label	Occurrences
Einstein–Maxwell equations canonical	3
Einstein–Maxwell theory	2
Einstein field equations with electromagnetic stress–energy tensor	1

Statements (51)

Predicate	Object
instanceOf	equations of motion ⓘ field equations ⓘ system of partial differential equations ⓘ theory in theoretical physics ⓘ
appliesTo	curved spacetime ⓘ spacetimes with charged matter ⓘ vacuum with electromagnetic fields ⓘ
assumes	classical (non-quantum) fields ⓘ general covariance ⓘ minimal coupling between gravity and electromagnetism ⓘ
basedOn	Einstein field equations ⓘ Maxwell's equations ⓘ surface form: Maxwell equations
describes	coupling of gravity and electromagnetism ⓘ interaction between spacetime curvature and electromagnetic fields ⓘ
expressedAs	G_{μν} = 8π T_{μν}^{(EM)} + 8π T_{μν}^{(matter)} ⓘ ∇_{[α} F_{βγ]} = 0 ⓘ ∇_{μ} F^{μν} = 4π J^{ν} ⓘ
field	classical electromagnetism ⓘ general relativity ⓘ gravitational physics ⓘ relativistic field theory ⓘ
formulatedIn	differential geometry ⓘ tensor calculus ⓘ
hasPart	Einstein–Maxwell equations self-linksurface differs ⓘ surface form: Einstein field equations with electromagnetic stress–energy tensor Maxwell equations with covariant derivatives ⓘ source-free Maxwell equations in curved spacetime ⓘ
involvesQuantity	Ricci curvature tensor R_{μν} ⓘ current four-vector J^{μ} ⓘ electromagnetic field tensor F_{μν} ⓘ electromagnetic stress–energy tensor T_{μν}^{(EM)} ⓘ metric tensor g_{μν} ⓘ scalar curvature R ⓘ
relatedTo	Einstein field equations ⓘ surface form: Einstein equations Einstein–Yang–Mills equations ⓘ Kaluza–Klein theory ⓘ Maxwell's equations ⓘ surface form: Maxwell equations classical field theory ⓘ
satisfies	Bianchi identities through Einstein tensor ⓘ local charge conservation ⓘ
usedFor	Kerr–Newman black hole ⓘ surface form: Kerr–Newman solution Reissner–Nordström metric ⓘ surface form: Reissner–Nordström solution electrovacuum solutions ⓘ modeling charged black holes ⓘ relativistic stellar models with charge ⓘ studying gravitational waves with electromagnetic fields ⓘ
uses	Einstein tensor ⓘ Levi-Civita connection ⓘ Lorentzian metric ⓘ covariant derivative ⓘ electromagnetic field tensor ⓘ stress–energy tensor ⓘ

Referenced by (6)

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

Reissner–Nordström metric → solves → Einstein–Maxwell equations ⓘ

Kerr–Newman black hole → solutionOf → Einstein–Maxwell equations ⓘ

Israel–Carter–Robinson uniqueness theorems → assumes → Einstein–Maxwell equations ⓘ

this entity surface form: Einstein–Maxwell theory

Einstein–Maxwell equations → hasPart → Einstein–Maxwell equations self-linksurface differs ⓘ

this entity surface form: Einstein field equations with electromagnetic stress–energy tensor

Einstein–Yang–Mills equations → generalizes → Einstein–Maxwell equations ⓘ

Kaluza–Klein theory → generalizationOf → Einstein–Maxwell equations ⓘ

this entity surface form: Einstein–Maxwell theory