On the uniqueness of Schwarzschild-de Sitter spacetime

Autor(en)

Stefano Borghini, Piotr T. Chrusciel, Lorenzo Mazzieri

Abstrakt

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(en)

Gravitationsphysik

Externe Organisation(en)

Università degli Studi di Milano-Bicocca, Università degli Studi di Trento

Journal

Archive for Rational Mechanics and Analysis

Band

247

Anzahl der Seiten

35

ISSN

0003-9527

Publikationsdatum

10-2021

Peer-reviewed

Ja

ÖFOS 2012

101006 Differentialgeometrie

ASJC Scopus Sachgebiete

Mechanical Engineering, Analysis, Mathematics (miscellaneous)

Link zum Portal

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