Conical spacetimes and global hyperbolicity

TL;DR

This paper investigates the properties of conical spacetimes, focusing on their global hyperbolicity, metric splitting, and the structure of Cauchy hypersurfaces and causal curves, extending previous work on wave equations.

Contribution

It advances understanding by analyzing metric splitting and causal structures in conical spacetimes, complementing prior results on wave equation well-posedness.

Findings

Confirmed global hyperbolicity of conical spacetimes

Explored metric splitting and Cauchy hypersurfaces

Provided preliminary insights into causal curves

Abstract

Vickers and Wilson (see Ref. 25) have shown global hyperbolicity of the conical spacetime in the sense of well-posedness of the initial value problem for the wave equation in generalized functions. We add the aspect of metric splitting and preliminary thoughts on Cauchy hypersurfaces and causal curves.