On the classification of static vacuum metrics in presence of a cosmological constant

Part II - Riemannian Penrose Inequality for static metrics with positive cosmological constant

April 19, 2017
Versione stampabile

Venue: Room A107 – Polo Scientifico Tecnologico “F. Ferrari”
Time: 14:00

  • Speaker: Lorenzo Mazzieri (University of Trento)

Abstract:
Static vacuum metrics probably represent the most basic objects in General Relativity. In fact they are solutions to the Einstein Field Equations with vanishing Stress-Energy tensor (vacuum), featuring a very special metric structure (warped product). Such a structure induces a natural foliation of the spacetime into space-like slices which are all isometric to each other, so that the corresponding physical universe is static. For static metrics with positive cosmological constant, we recall the notion of virtual mass introduced in the first part of the seminar, where a Positive Mass Statement was also proved. Building on this, we provide in this context also the precise analog of the Riemannian Penrose Inequality. Time permitting, we show how to employ these instruments in order to obtain a Uniqueness Theorem for the Schwarzschild-de Sitter solution among the static black holes obeying to some natural conditions.