Spacelike Causal Boundary at Finite Distance and Continuous Extension of the Metric: A Preliminary Report

Harris, Stacey (Steven) G.

doi:10.1007/978-3-031-05379-5_9

Cited by 1 publication

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“…Independent of trying to replace the ∂ − ι(M ) = ∅ assumption with ∂ + ι(M ) ∩ ∂ − ι(M ) = ∅ it would be nice to obtain a better understanding of how our extensions fit in with these older boundary constructions in general and recent efforts by Harris to find sufficient conditions guaranteeing a nice, spacelike c-boundary at finite distance (cf. [11]), which feels at least similar in spirit to our approach, in particular.…”

Section: Discussionsupporting

confidence: 72%

Uniqueness of Maximal Spacetime Boundaries

Graf,

van den Beld-Serrano

2024

Ann. Henri Poincaré

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Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski [22], where he obtains local uniqueness results for anchored spacetime extensions of similar character to earlier work for conformal boundaries by Chruściel [2]. Globally, it is known that non-uniqueness can arise from timelike geodesics behaving pathologically in the sense that there exist points along two distinct timelike geodesics which become arbitrarily close to each other interspersed with points which do not approach each other. We show that this is in some sense the only obstruction to uniqueness of maximal future boundaries: Working with extensions that are manifolds with boundary we prove that, under suitable assumptions on the regularity of the considered extensions and excluding the existence of such “intertwined timelike geodesics”, extendible spacetimes admit a unique maximal future boundary extension. This is analogous to results of Chruściel for the conformal boundary.

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Section: Discussionsupporting

confidence: 72%