This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as the only static vacuum metric with zero mass. In this second part, we prove optimal area bounds for horizons of black hole type and of cosmological type, corresponding to Riemannian Penrose inequalities and to cosmological area bounds à la Boucher–Gibbons–Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild–de Sitter spacetime.

Borghini, S., Mazzieri, L. (2020). On the Mass of Static Metrics with Positive Cosmological Constant: II. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 377(3), 2079-2158 [10.1007/s00220-020-03739-8].

On the Mass of Static Metrics with Positive Cosmological Constant: II

Borghini, Stefano
;
2020

Abstract

This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as the only static vacuum metric with zero mass. In this second part, we prove optimal area bounds for horizons of black hole type and of cosmological type, corresponding to Riemannian Penrose inequalities and to cosmological area bounds à la Boucher–Gibbons–Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild–de Sitter spacetime.
Articolo in rivista - Articolo scientifico
Static metrics, Schwarzschild de Sitter solution, Riemannian Penrose Inequality, Black Hole Uniqueness Theorem;
English
7-apr-2020
2020
377
3
2079
2158
open
Borghini, S., Mazzieri, L. (2020). On the Mass of Static Metrics with Positive Cosmological Constant: II. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 377(3), 2079-2158 [10.1007/s00220-020-03739-8].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/314212
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