English

Isometries of spacetimes without observer horizons

Differential Geometry 2026-03-25 v3 General Relativity and Quantum Cosmology Mathematical Physics math.MP

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, Z\mathbb{Z}, or R\mathbb{R}.

Keywords

Cite

@article{arxiv.2502.13904,
  title  = {Isometries of spacetimes without observer horizons},
  author = {Leonardo García-Heveling and Abdelghani Zeghib},
  journal= {arXiv preprint arXiv:2502.13904},
  year   = {2026}
}

Comments

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