Causality violation and singularities

TL;DR

This paper demonstrates that singularities are inevitable in space-times with causality-violating boundaries under certain conditions, relaxing the usual global causality assumption in Hawking-Penrose theorems.

Contribution

It introduces restrictions on causality-violating sets to establish the occurrence of singularities without requiring global causality.

Findings

Singularities occur when causality-violating boundaries exist.

Restrictions on causality-violating sets can replace global causality assumptions.

Singularities are shown to be unavoidable under these conditions.

Abstract

We show that singularities necessarily occur when a boundary of causality violating set exists in a space-time under the physically suitable assumptions except the global causality condition in the Hawking-Penrose singularity theorems. Instead of the global causality condition, we impose some restrictions on the causality violating sets to show the occurrence of singularities.