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

How this entity was disambiguated

This entity first appeared as the object of triple T623092 — 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: Einstein–Maxwell equations
Context triple: [Reissner–Nordström metric, solves, Einstein–Maxwell equations]

A. Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
B. Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
C. Maxwell stress tensor
The Maxwell stress tensor is a mathematical construct in classical electromagnetism that represents how electric and magnetic fields transmit mechanical stresses, such as pressure and tension, through space and matter.
D. Reissner–Nordström metric
The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.
E. Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
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: Einstein–Maxwell equations
Target entity description: 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.

A. Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
B. Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
C. Maxwell stress tensor
The Maxwell stress tensor is a mathematical construct in classical electromagnetism that represents how electric and magnetic fields transmit mechanical stresses, such as pressure and tension, through space and matter.
D. Reissner–Nordström metric
The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.
E. Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
F. None of above. chosen

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 ⓘ

How these facts were elicited

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 ⓘ