Einstein–Hilbert action

E287408

action functional concept in general relativity gravitational action

The Einstein–Hilbert action is the fundamental action in general relativity whose variation yields Einstein’s field equations, expressing gravity as the dynamics of spacetime curvature.

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All labels observed (6)

Label	Occurrences
Einstein–Hilbert action canonical	4
Einstein–Hilbert Lagrangian density	1
Einstein–Hilbert action (on shell)	1
Einstein–Hilbert action with Yang–Mills term	1
Hilbert action	1
Palatini action	1

How this entity was disambiguated

This entity first appeared as the object of triple T2683206 — 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–Hilbert action
Context triple: [Ricci scalar, appearsIn, Einstein–Hilbert action]

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. Nambu–Goto action
The Nambu–Goto action is a fundamental formulation in string theory that describes the dynamics of relativistic strings by minimizing the area of their worldsheet in spacetime.
C. Wheeler–DeWitt equation
The Wheeler–DeWitt equation is a fundamental equation in quantum gravity that attempts to describe the quantum state of the entire universe without reference to time.
D. Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
E. Einstein–Maxwell equations
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.
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–Hilbert action
Target entity description: The Einstein–Hilbert action is the fundamental action in general relativity whose variation yields Einstein’s field equations, expressing gravity as the dynamics of spacetime curvature.

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. Nambu–Goto action
The Nambu–Goto action is a fundamental formulation in string theory that describes the dynamics of relativistic strings by minimizing the area of their worldsheet in spacetime.
C. Wheeler–DeWitt equation
The Wheeler–DeWitt equation is a fundamental equation in quantum gravity that attempts to describe the quantum state of the entire universe without reference to time.
D. Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
E. Einstein–Maxwell equations
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.
F. None of above. chosen

Statements (47)

Predicate	Object
instanceOf	action functional ⓘ concept in general relativity ⓘ gravitational action ⓘ
assumes	metric compatibility of Levi-Civita connection ⓘ torsion-free connection in standard formulation ⓘ
codomain	real numbers ⓘ
defines	dynamics of spacetime curvature ⓘ
dependsOn	Ricci scalar ⓘ determinant of the metric tensor ⓘ spacetime metric ⓘ
describes	classical gravitational field ⓘ
domain	space of Lorentzian metrics on a manifold ⓘ
field	differential geometry ⓘ general relativity ⓘ mathematical physics ⓘ theoretical physics ⓘ
formulatedIn	Riemannian geometry ⓘ linked to: Riemannian manifolds tensor calculus ⓘ
generalizedTo	f(R) gravity ⓘ higher-derivative gravity theories ⓘ
givesEquationsOfMotion	Einstein tensor equals stress–energy tensor ⓘ
historicalContext	development of general relativity ⓘ
historicalDevelopment	formulated in 1915 ⓘ
includesConstant	Newtonian gravitational constant G ⓘ factor 1 over 16πG ⓘ speed of light c ⓘ
integrandContains	Ricci scalar R ⓘ square root of minus determinant of metric ⓘ
integratedOver	four-dimensional spacetime manifold ⓘ
invariantUnder	diffeomorphisms ⓘ
isGenerallyCovariant	true ⓘ
isSumOf	matter action ⓘ pure gravitational action ⓘ
mathematicalObjectType	scalar functional of the metric ⓘ
mayIncludeTerm	cosmological constant ⓘ
namedAfter	Albert Einstein ⓘ David Hilbert ⓘ
relatedConcept	Hilbert action ⓘ linked to: Einstein–Hilbert action Lagrangian density for gravity ⓘ Palatini action ⓘ linked to: Einstein–Hilbert action
usedAs	starting point for modified gravity theories ⓘ
usedIn	classical limit of quantum gravity approaches ⓘ derivation of Einstein field equations ⓘ path integral formulation of gravity ⓘ
variationPrinciple	stationary action principle ⓘ
variationWithRespectTo	metric tensor ⓘ
yieldsViaVariation	Einstein field equations ⓘ

How these facts were elicited