Conformal boundary extensions of Lorentzian manifolds

TL;DR

This paper investigates the uniqueness and existence of conformal boundary extensions of Lorentzian manifolds, providing conditions for maximal completions and applications to space-time classification and mass definition.

Contribution

It establishes local and global criteria for the uniqueness of boundary extensions based on null geodesics, including new results on maximal spacelike and strongly causal boundaries.

Findings

Proves local uniqueness of boundary extensions.

Provides necessary and sufficient conditions for maximal completions.

Demonstrates applications to space-time classification and mass definition.

Abstract

We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of unique maximal completions. The condition is verified in several situations of interest. This leads to existence and uniqueness of maximal spacelike conformal boundaries, of maximal strongly causal boundaries, as well as uniqueness of conformal boundary extensions for asymptotically simple space-times. Examples of applications include the definition of mass, or the classification of inequivalent extensions across a Cauchy horizon of the Taub space-time.