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://ucrisportal.univie.ac.at/en/publications/a4d363e0-95f1-4611-86f4-96f86b1e8e2d