Open Access
January 2010 Conformal boundary extensions of Lorentzian manifolds
Piotr T. Chrúsciel
J. Differential Geom. 84(1): 19-44 (January 2010). DOI: 10.4310/jdg/1271271792


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.


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Piotr T. Chrúsciel. "Conformal boundary extensions of Lorentzian manifolds." J. Differential Geom. 84 (1) 19 - 44, January 2010.


Published: January 2010
First available in Project Euclid: 14 April 2010

zbMATH: 1198.53081
MathSciNet: MR2629508
Digital Object Identifier: 10.4310/jdg/1271271792

Rights: Copyright © 2010 Lehigh University

Vol.84 • No. 1 • January 2010
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