Energy density and spatial curvature in general relativity

Theodore Frankel, Gregory J Galloway

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Positive energy density tends to limit the size of space. This effect is studied within several contexts. We obtain sufficient conditions (which involve the energy density in a crucial way) for the compactness of spatial hypersurfaces in space-time. We then obtain some results concerning static or, more generally, stationary space-times. The Schwarzchild solution puts an upper bound on the size of a static spherically symmetric fluid with density bounded from below. We derive a result of roughly the same nature which, however, requires no symmetry and allows for rotation. Also, we show that static or rotating universes with Λ=0 require that the density along some spatial geodesic must fall off rapidly with distance from a point.

Original languageEnglish (US)
Pages (from-to)813-817
Number of pages5
JournalJournal of Mathematical Physics
Volume22
Issue number4
StatePublished - 1980

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Relativity
General Relativity
Energy Density
relativity
flux density
Curvature
curvature
Fluids
Space-time
void ratio
Geodesic
Hypersurface
Compactness
Rotating
universe
Tend
Upper bound
Symmetry
Fluid
Sufficient Conditions

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Energy density and spatial curvature in general relativity. / Frankel, Theodore; Galloway, Gregory J.

In: Journal of Mathematical Physics, Vol. 22, No. 4, 1980, p. 813-817.

Research output: Contribution to journalArticle

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