Computability of the causal boundary by using isocausality

TL;DR

This paper explores how the causal boundary in mathematical relativity can be computed using isocausality, providing a framework to compare spacetimes and analyze their causal structures.

Contribution

It introduces a new framework for isocausal comparisons with standard stationary spacetimes to analyze the causal boundary's behavior.

Findings

Qualitative behavior of the c-boundary is characterized for a wide class of spacetimes.

Framework allows comparison of causal boundaries via isocausality.

Insights into the relationship between causal and conformal boundaries.

Abstract

Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the present paper, we consider the notion of isocausality given by Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out isocausal comparisons with standard stationary spacetimes. As a consequence, the qualitative behavior of the c-boundary (at the three levels: point set, chronology and topology) of a wide class of spacetimes, is obtained.