positive mass theorem

E603722

mathematical theorem result in differential geometry result in general relativity

The positive mass theorem is a fundamental result in differential geometry and general relativity stating that, under suitable conditions, the total mass of an isolated gravitational system is nonnegative and vanishes only for flat spacetime.

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All labels observed (2)

Label	Occurrences
positive mass theorem canonical	1
positive mass theorem in general relativity	1

Statements (47)

Predicate	Object
instanceOf	mathematical theorem ⓘ result in differential geometry ⓘ result in general relativity ⓘ
alsoKnownAs	positive energy theorem NERFINISHED ⓘ
alternativeProofMethod	spinor methods ⓘ
appliesTo	initial data sets for Einstein field equations ⓘ time-symmetric initial data in the Riemannian case ⓘ
asserts	total mass is nonnegative under suitable conditions ⓘ total mass vanishes only for flat spacetime ⓘ
assumes	asymptotically flat spacetime ⓘ dominant energy condition ⓘ
concerns	ADM mass ⓘ Bondi mass NERFINISHED ⓘ total mass of an isolated gravitational system ⓘ
ensures	ADM mass is nonnegative for suitable asymptotically flat manifolds NERFINISHED ⓘ
field	differential geometry ⓘ general relativity NERFINISHED ⓘ mathematical relativity ⓘ
firstCompleteProofYear	1979 ⓘ
generalizedBy	positive mass theorem in higher dimensions ⓘ positive mass theorem with charge NERFINISHED ⓘ
hasVersion	Lorentzian positive mass theorem NERFINISHED ⓘ Riemannian positive mass theorem NERFINISHED ⓘ minimal surface proof version ⓘ spinorial proof version ⓘ
implies	Minkowski spacetime is the unique zero-mass solution under the hypotheses NERFINISHED ⓘ no negative-mass isolated gravitational systems under the hypotheses ⓘ stability of Minkowski spacetime with respect to mass ⓘ
influenced	geometric analysis ⓘ global differential geometry ⓘ mathematical foundations of general relativity ⓘ
originalProofMethod	minimal surface techniques ⓘ
provedBy	Edward Witten NERFINISHED ⓘ Richard Schoen NERFINISHED ⓘ Shing-Tung Yau NERFINISHED ⓘ
relatedTo	Penrose inequality NERFINISHED ⓘ Yamabe problem NERFINISHED ⓘ cosmic censorship conjecture NERFINISHED ⓘ
requiresCondition	appropriate decay of the metric at infinity ⓘ nonnegative scalar curvature in the Riemannian version ⓘ
spinorialProofYear	1981 ⓘ
usesConcept	ADM 4-momentum NERFINISHED ⓘ asymptotically flat Riemannian manifold ⓘ energy conditions ⓘ scalar curvature ⓘ
zeroMassCase	manifold is isometric to Euclidean space in the Riemannian version ⓘ spacetime is isometric to Minkowski spacetime in the Lorentzian version ⓘ

Referenced by (2)

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

Richard Schoen → notableWork → positive mass theorem ⓘ

Shing-Tung Yau → knownFor → positive mass theorem ⓘ

this entity surface form: positive mass theorem in general relativity