In a distinguishing spacetime the horismos relation generates the causal relation

Details In a distinguishing spacetime the horismos relation generates the causal relation In a distinguishing spacetime the horismos relation generates the causal relation

2009-04-21

arxiv.org/abs/0904.3263v1

Class.Quant.Grav.26:165005,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, Latex2e

Scientific paper

10.1088/0264-9381/26/16/165005

It is proved that in a distinguishing spacetime the horismos relation E^+=J^+\I^+ generates the causal relation J^+. In other words two causally related events are joined by a chain of horismotically related events, or again, the causal relation is the smallest transitive relation containing the horismos relation. The result is sharp in the sense that distinction can not be weakened to future or past distinction. Finally, it is proved that a spacetime in which the horismos relation generates the causal relation is necessarily non-total imprisoning.

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