Causal Stability Conditions for General Relativistic Spacetimes

TL;DR

This paper explores the causal structure of general relativistic spacetimes, introducing the concept of almost stable causality and examining conditions for causal stability and potential violations.

Contribution

It introduces the novel concept of almost stable causality and discusses new criteria for assessing the stability of causal structures in general relativity.

Findings

Introduction of almost stable causality concept

Discussion of conditions for causal stability

Analysis of potential causality violations

Abstract

A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the problem of fundamental causal stability conditions. Several questions are raised and some of the potential consequences of recent results regarding the causality problem in general relativity are presented. A key question is whether causality violating regions are locally allowed. The new concept of almost stable causality is introduced; meanwhile, related conditions and criteria for the stability and almost stability of the causal structure are discussed.