On the uniqueness of Schwarzschild-de Sitter spacetime

Stefano Borghini, Piotr T. Chrusciel, Lorenzo Mazzieri (Corresponding author)

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Abstract

We establish a new uniqueness theorem for the three dimensional Schwarzschild–de Sitter metrics. For this, some new or improved tools are developed. These include a reverse Łojasiewicz inequality, which holds in a neighborhood of the extremal points of any smooth function. We further prove the smoothness of the set of maxima of the lapse, whenever this set contains a topological hypersurface. This leads to a new strategy for the classification of well behaved static solutions of vacuum Einstein equations with a positive cosmological constant, based on the geometry of the maximum-set of the lapse.

Original languageEnglish
Article number22
Number of pages35
JournalArchive for Rational Mechanics and Analysis
Volume247
Issue number2
DOIs
Publication statusPublished - 9 Mar 2023

Austrian Fields of Science 2012

  • 101006 Differential geometry

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