Isometries of spacetimes without observer horizons

Abstract

We study the isometry groups of (non-compact) Lorentzian manifolds with well-behaved causal structure, aka causal spacetimes satisfying the ``no observer horizons'' condition. Our main result is that the group of time orientation-preserving isometries acts properly on the spacetime. As corollaries, we obtain the existence of an invariant Cauchy temporal function, and a splitting of the isometry group into a compact subgroup and a subgroup roughly corresponding to time translations. The latter can only be the trivial group, $\mathbb{Z}$, or $\mathbb{R}$.

21 pages, 4 figures. Changes in v3: Added Section 2.4 about physical context, modified argument in proof of Prop 2.7, and other minor improvements throughout the text

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Cited by in corpus (1)

• Differentiability and Other Properties of the Cosmological Volume Function