|Location:||MSRI: Simons Auditorium|
Asymptotically hyperbolic manifolds appear in many situations in General Relativity, such as isolated systems in a universe with negative cosmological constant and in the AdS/CFT correspondence theory as conformally compact spaces.
As for the ADM mass of asymptotically Euclidean manifolds, one can define mass-like asymptotic invariants. After a review of classical results about these quantities such as positive mass theorems by X. Wang and P.T. Chrusciel - M. Herzlich, we will focus on the mass-aspect tensor that appears in Wang's definition, when the boundary at infinity is assumed to be spherical.
We will give examples for Kottler-Schwarzschild-AdS manifolds as well as a new family which has interesting properties near infinity, such as being conformally flat and of constant scalar curvature. We will finally discuss how to look for new mass-like invariants constructed from the mass-aspect tensor.
This is partly based on a joint work with Mattias Dahl and Romain Gicquaud.