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.

Aliases (2)

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 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 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 equations → Einstein–Yang–Mills equations → Kaluza–Klein theory → Maxwell equations → classical field theory →
satisfies	Bianchi identities through Einstein tensor → local charge conservation →
usedFor	Kerr–Newman solution → 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 (4)

Subject (surface form when different)	Predicate
Israel–Carter–Robinson uniqueness theorems ("Einstein–Maxwell theory") →	assumes
Einstein–Maxwell equations ("Einstein field equations with electromagnetic stress–energy tensor") →	hasPart
Kerr–Newman black hole →	solutionOf
Reissner–Nordström metric →	solves