On the Curvature and Topology of Compact Stationary Spacetimes

TL;DR

This paper investigates the geometric and topological constraints of compact stationary spacetimes with a timelike Killing vector, building on recent results to identify obstructions to certain curvature and topology configurations.

Contribution

It provides new obstructions to the curvature and topology of compact stationary spacetimes, extending the understanding of their geometric structure.

Findings

Identifies specific obstructions to curvature in compact stationary spacetimes.

Establishes topological constraints related to the existence of a timelike Killing vector.

Builds on recent results to deepen the understanding of Lorentzian manifold geometry.

Abstract

Using the result of Petersen & Wink '21, we find obstructions to the curvature and topology of compact Lorentzian manifolds admitting a unit-length timelike Killing vector field.