In this paper we prove a new uniqueness result for the de Sitter solution. Our theorem is based on a new notion of mass, whose well-posedness is discussed and established in the realm of static spacetimes with positive cosmological constant that are bounded by Killing horizons. This new definition is formulated in terms of the surface gravities of the Killing horizons and agrees with the usual notion when the Schwarzschild-de Sitter solutions are considered. A positive mass statement is also shown to hold in this context. The corresponding rigidity statement coincides with the above mentioned characterization of the de Sitter solution as the only static vacuum metric with zero mass. Finally, exploiting some particular features of our formalism, we show how the same analysis can be fruitfully employed to treat the case of negative cosmological constant, leading to a new uniqueness theorem for the anti-de Sitter spacetime, which holds under a very feeble assumption on the asymptotic behavior of the solution.

Borghini, S., Mazzieri, L. (2018). On the mass of static metrics with positive cosmological constant: I. CLASSICAL AND QUANTUM GRAVITY, 35(12) [10.1088/1361-6382/aac081].

On the mass of static metrics with positive cosmological constant: I

Borghini, Stefano
;
2018

Abstract

In this paper we prove a new uniqueness result for the de Sitter solution. Our theorem is based on a new notion of mass, whose well-posedness is discussed and established in the realm of static spacetimes with positive cosmological constant that are bounded by Killing horizons. This new definition is formulated in terms of the surface gravities of the Killing horizons and agrees with the usual notion when the Schwarzschild-de Sitter solutions are considered. A positive mass statement is also shown to hold in this context. The corresponding rigidity statement coincides with the above mentioned characterization of the de Sitter solution as the only static vacuum metric with zero mass. Finally, exploiting some particular features of our formalism, we show how the same analysis can be fruitfully employed to treat the case of negative cosmological constant, leading to a new uniqueness theorem for the anti-de Sitter spacetime, which holds under a very feeble assumption on the asymptotic behavior of the solution.
Articolo in rivista - Articolo scientifico
static metrics, (Anti) de Sitter solution, positive mass theorem;
English
2018
35
12
125001
open
Borghini, S., Mazzieri, L. (2018). On the mass of static metrics with positive cosmological constant: I. CLASSICAL AND QUANTUM GRAVITY, 35(12) [10.1088/1361-6382/aac081].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/314203
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