Volume functions in general relativity.

Details Volume functions in general relativity. Volume functions in general relativity.

Sep 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988gregr..20..859d&link_type=abstract

General Relativity and Gravitation, Volume 20, Issue 9, pp.859-867

Mathematics

Logic

8

General Relativity

Scientific paper

It is shown that on every spacetime there is a finite Borel measure such that open sets have positive measure and the topological boundary of the chronological past/future of every point has measure zero. Using this measure volume, functions are defined. It is shown that they are semicontinuous, and the set of points at which they are discontinuous is a union of nullgeodesics. The following causality conditions are characterized in terms of their properties: chronological, distinguishing, strongly causal, causally continuous, globally hyperbolic.

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