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

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.

64 pages, 6 figures. Results in Subsection 1.4 revised and improved

References in corpus (12)

• Coding Theorem and Strong Converse for Quantum Channels
• Hypercontractivity of quasi-free quantum semigroups
• Adventures in de Sitter space
• On the mass of static metrics with positive cosmological constant - I
• Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant
• Positive mass theorems for asymptotically de Sitter spacetimes
• Estimating the decoherence time using non-commutative Functional Inequalities
• Positive Scalar Curvature and Minimal Hypersurface Singularities
• Strong converse bounds in quantum network information theory: distributed hypothesis testing and source coding
• Strong Converse for Classical-Quantum Degraded Broadcast Channels
• Hypercontractivity and logarithmic Sobolev Inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates
• Brown-York mass and positive scalar curvature I - First eigenvalue problem and its applications

Cited by in corpus (8)

• On the mass of static metrics with positive cosmological constant - I
• On the uniqueness of Schwarzschild-de Sitter spacetime
• Asymptotics with a cosmological constant: The solution space
• Static Black Hole Uniqueness for nonpositive masses
• Anisotropic $p$-capacity and anisotropic Minkowski inequality
• On the Serrin problem for ring-shaped domains
• Symmetry results for Serrin-type problems in doubly connected domains
• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes