Conformal boundary extensions of Lorentzian manifolds

Chrusciel, Piotr T.

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Conformal boundary extensions of Lorentzian manifolds

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Chrusciel, Piotr T.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Chrusciel, P. T. (2010). Conformal boundary extensions of Lorentzian manifolds. Journal of Differential Geometry, 84, 19-44. Retrieved from http://projecteuclid.org/euclid.jdg/1271271792.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5F92-0

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.