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6 - Causal structure

Published online by Cambridge University Press:  17 February 2023

Stephen W. Hawking  and
George F. R. Ellis
Stephen W. Hawking
Affiliation:
University of Cambridge
George F. R. Ellis
Affiliation:
University of Cape Town
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Summary

§6.1 deals with the question of the orientability of timelike and spacelike bases. In §6.2 basic causal relations are defined and the definition of a non-spacelike curve is extended from piecewise differentiable to continuous. The properties of the boundary of the future of a set are derived in §6.3. In §6.4a number of conditions which rule out violations or near violations of causality are discussed. The closely related concepts of Cauchy developments and global hyperbolicity are introduced in §6.5 and §6.6, and are used in §6.7 to prove the existence of non-spacelike geodesies of maximum length between certain pairs of points.

In §6.8 we describe the construction of Geroch, Kronheimer, and Penrose for attaching a causal boundary to spacetime. A particular example of such a boundary is provided by a class of asymptotically flat spacetimes which are studied in § 6.9

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The Large Scale Structure of Space-Time
50th Anniversary Edition
 , pp. 180 - 225
Publisher: Cambridge University Press
Print publication year: 2023

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