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

Abstract

In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leading to a uniqueness theorem for the Anti de Sitter spacetime.

34 pages, 3 figures

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• On the mass of static metrics with positive cosmological constant - I
• On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds
• On the uniqueness of Schwarzschild-de Sitter spacetime
• Quantum reverse hypercontractivity: its tensorization and application to strong converses
• On the mass of static metrics with positive cosmological constant -- II
• Asymptotics with a cosmological constant: The solution space
• A Green's function proof of the Positive Mass Theorem
• Uniqueness and energy bounds for static AdS metrics
• Static Black Hole Uniqueness for nonpositive masses
• Anisotropic $p$-capacity and anisotropic Minkowski inequality
• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
• On the Serrin problem for ring-shaped domains
• Symmetry results for Serrin-type problems in doubly connected domains
• Geometric inequalities for critical metrics of the volume functional