Relating a Geroch-like boundary and the abstract boundary constructions for spacetimes

TL;DR

This paper introduces a new Geroch-like boundary for spacetimes, demonstrating its natural embedding into the Scott-Szekeres abstract boundary, thus linking two prominent boundary constructions in a natural manner.

Contribution

It constructs a Geroch-like boundary, denoted by ig, and explicitly embeds it into the Scott-Szekeres abstract boundary, establishing a natural relation between the two boundary concepts.

Findings

Constructed a Geroch-like boundary ig for spacetimes.

Established an explicit, natural embedding of ig into the Scott-Szekeres boundary.

Answered affirmatively the question of a natural relation between the g and a boundary constructions.

Abstract

We construct a Geroch-like boundary (when restricted to geodesic curves, this boundary contains as a subset the Geroch's $g$ boundary), which we denote by $\tilde{g}$, and establish an explicit embedding of the $\tilde{g}$ boundary into the $a$ boundary of Scott and Szekeres. This construction, and subsequently the explicit embedding, is done in a 'natural' way (the emphasis on the word natural here will be clarified in the text), thereby answering in the affirmative the outstanding question as to whether there exists a natural way to relate the $g$ and the $a$ boundary constructions.