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 ⓘ

How these facts were elicited

The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.

Instruction

You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10.

# Requirements
- If you don't know the subject at all, return an empty list.
- If the subject is not a named entity, return an empty list.
- Include at least one triple where predicate is "instanceOf".
- Do not get too wordy.
- Separate several objects into multiple triples with one object.

Input

Subject: Einstein–Maxwell equations
Description of subject: 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.

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