Causally simple spacetimes and naked singularities

TL;DR

This paper proves a conjecture linking naked singularities to non-Hausdorff spaces of null geodesics and characterizes two-dimensional causally simple spacetimes as null pseudoconvex, with implications for higher dimensions.

Contribution

It establishes a connection between naked singularities and the topology of null geodesic spaces, and characterizes 2D causally simple spacetimes as null pseudoconvex.

Findings

Naked singularities imply non-Hausdorff null geodesic spaces.

Two-dimensional causally simple spacetimes are null pseudoconvex.

Counterexamples exist in higher dimensions.

Abstract

In this paper, We prove a conjecture which states that if M is a nakedly singular future boundary or nakedly singular past boundary spacetime, then the space of null geodesics, N, is non-Hausdorff. Also, we show that every two-dimensional strongly causal spacetime M is causally simple if and only if it is null pseudoconvex. As a result, it implies the converse of the conjecture for two-dimension but there are examples that refute it for more dimensions.