Existence of standard splittings for conformally stationary spacetimes

Details Existence of standard splittings for conformally stationary spacetimes Existence of standard splittings for conformally stationary spacetimes

2008-06-04

arxiv.org/abs/0806.0812v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages

Scientific paper

Let $(M,g)$ be a spacetime which admits a complete timelike conformal Killing vector field $K$. We prove that $(M,g)$ splits globally as a standard conformastationary spacetime with respect to $K$ if and only if $(M,g)$ is distinguishing (and, thus causally continuous). Causal but non-distinguishing spacetimes with complete stationary vector fields are also exhibited. For the proof, the recently solved ``folk problems'' on smoothability of time functions (moreover, the existence of a {\em temporal} function) are used.

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