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.

On the Uniqueness of Schwarzschild–de Sitter Spacetime / Borghini, Stefano; Chruściel, Piotr T.; Mazzieri, Lorenzo. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 247:2(2023), pp. 2201-2235. [10.1007/s00205-023-01860-1]

On the Uniqueness of Schwarzschild–de Sitter Spacetime

Borghini, Stefano;Mazzieri, Lorenzo
2023-01-01

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.
2023
2
Borghini, Stefano; Chruściel, Piotr T.; Mazzieri, Lorenzo
On the Uniqueness of Schwarzschild–de Sitter Spacetime / Borghini, Stefano; Chruściel, Piotr T.; Mazzieri, Lorenzo. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 247:2(2023), pp. 2201-2235. [10.1007/s00205-023-01860-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/404771
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