### 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 language | English (US) |
---|---|

Pages (from-to) | 813-817 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 22 |

Issue number | 4 |

State | Published - 1980 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*22*(4), 813-817.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 22, no. 4, pp. 813-817.

}

TY - JOUR

T1 - Energy density and spatial curvature in general relativity

AU - Frankel, Theodore

AU - Galloway, Gregory J

PY - 1980

Y1 - 1980

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039612948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039612948&partnerID=8YFLogxK

M3 - Article

VL - 22

SP - 813

EP - 817

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

ER -