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An intrinsic conformal Lorentz pseudodistance

Published online by Cambridge University Press:  24 October 2008

Michael J Markowitz
Michael J Markowitz
Affiliation:
University of Chicago
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Abstract

An intrinsic pseudodistance dM is associated to the underlying causal structure of a Lorentzian manifold (M, g). An infinitesimal form for dM is defined on the bundle of null vectors over M and is used to prove that, under certain physically reasonable energy conditions, M is conformally hyperbolic, i.e. that dM is a true distance. As a corollary we obtain sufficient conditions for the conformal hyperbolicity of a globally hyperbolic space-time. Some exact solutions of the Einstein field equations are discussed and possible applications to the study of singularities are outlined.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 359 - 371
Copyright
Copyright © Cambridge Philosophical Society 1981

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