On the uniqueness of Schwarzschild-de Sitter spacetime

Author(s)
Stefano Borghini, Piotr T. Chrusciel, Lorenzo Mazzieri
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.

Organisation(s)
Gravitational Physics
External organisation(s)
Università degli Studi di Milano-Bicocca, Università degli Studi di Trento
Journal
Archive for Rational Mechanics and Analysis
Volume
247
No. of pages
35
ISSN
0003-9527
Publication date
10-2021
Peer reviewed
Yes
Austrian Fields of Science 2012
101006 Differential geometry
ASJC Scopus subject areas
Mechanical Engineering, Analysis, Mathematics (miscellaneous)
Portal url
https://ucris.univie.ac.at/portal/en/publications/on-the-uniqueness-of-schwarzschildde-sitter-spacetime(a4d363e0-95f1-4611-86f4-96f86b1e8e2d).html