Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds

TL;DR

This paper proves that certain inhomogeneous Lorentzian manifolds cannot admit infinite groups acting properly discontinuously and isometrically, highlighting limitations on symmetry groups in these spacetimes.

Contribution

It establishes the non-existence of infinite properly discontinuous isometric group actions on a class of inhomogeneous Lorentzian manifolds, extending previous results beyond homogeneous cases.

Findings

No infinite group acts properly discontinuously on these manifolds.

The result applies to a broad class of inhomogeneous Lorentzian manifolds.

It constrains the symmetry properties of certain Lorentzian geometries.

Abstract

In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.