Calculus of Variations and Geometric Measure Theory

S. Borghini - L. Mazzieri

On the mass of static metrics with positive cosmological constant - II

created by borghini on 07 Apr 2018
modified by mazzieri on 21 Feb 2023

[BibTeX]

Published Paper

Inserted: 7 apr 2018
Last Updated: 21 feb 2023

Journal: Communications in Mathematical Physics
Year: 2020
Doi: 10.1007/s00220-020-03739-8

ArXiv: 1711.07024 PDF

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 \`a la Boucher-Gibbons-Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild-de Sitter spacetime.