### 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) |
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Pages (from-to) | 813-817 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 22 |

Issue number | 4 |

State | Published - Dec 1 1980 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Mathematical Physics*,

*22*(4), 813-817.