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The topology of geodesically complete space-times

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Abstract

Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic toS 3 then the part of space-time that it encloses must be simply connected.

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  1. Department of Mathematics, Bolton Institute of Technology, Deane Road, BL3 5AB, Bolton, UK

    C. W. Lee

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  1. C. W. Lee
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Lee, C.W. The topology of geodesically complete space-times. Gen Relat Gravit 15, 21–30 (1983). https://doi.org/10.1007/BF00755892

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