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On the determination of Cauchy surfaces from intrinsic properties

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Abstract

We consider the problem of determining from intrinsic properties whether or not a given spacelike surface is a Cauchy surface. We present three results relevant to this question. First, we derive necessary and sufficient conditions for a compact surface to be a Cauchy surface in a spacetime which admits one. Second, we show that for a non-compact surface it is impossible to determine whether or not it is a Cauchy surface without imposing some restriction on the entire spacetime. Third, we derive conditions for an asymptotically flat surface to be a Cauchy surface by imposing the global condition that it be imbedded in a weakly asymptotically simple and empty spacetime.

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Authors and Affiliations

  1. Center for Theoretical Physics, Department of Physics and Astronomy, University of Maryland, 20742, College Park, Maryland, USA

    Robert Budic, James Isenberg, Lee Lindblom & Philip B. Yasskin

Authors
  1. Robert Budic
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  2. James Isenberg
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  3. Lee Lindblom
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  4. Philip B. Yasskin
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Additional information

Communicated by R. Geroch

This research was supported in part by the National Science Foundation grants PHY 70-022077 and PHY 76-20029 as well as the National Aeronautics and Space Administration grant NGR 21-002-010

National Science Foundation Pre-doctoral Fellow

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Budic, R., Isenberg, J., Lindblom, L. et al. On the determination of Cauchy surfaces from intrinsic properties. Commun.Math. Phys. 61, 87–95 (1978). https://doi.org/10.1007/BF01609469

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  • DOI: https://doi.org/10.1007/BF01609469

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