K-causality and degenerate spacetimes

Details K-causality and degenerate spacetimes K-causality and degenerate spacetimes

1999-12-21

arxiv.org/abs/gr-qc/9912090v1

Class.Quant.Grav. 17 (2000) 4377-4396

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 23 pages, 4 figures

Scientific paper

10.1088/0264-9381/17/21/303

The causal relation $K^+$ was introduced by Sorkin and Woolgar to extend the standard causal analysis of $C^2$ spacetimes to those that are only $C^0$. Most of their results also hold true in the case of spacetimes with degeneracies. In this paper we seek to examine $K^+$ explicitly in the case of Lorentzian topology changing Morse spacetimes containing isolated degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that $K^+$ is robust and that it coincides with the Seifert relation when the spacetime is stably causal. Moreover, the Hawking and Sachs characterisation of causal continuity translates into a natural expression in terms of $K^+$ for general spacetimes. We then examine $K^+$ in topology changing Morse spacetimes both with and without the degeneracies and find further characterisations of causal continuity.

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