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## Seminar on

**Mathematical General Relativity**

*Organizers:*

* *Philippe G. LeFloch *(Paris) *

*Ghani Zeghib (Lyon)*

**ANR Project**

#### “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

**February 20, 2013**

### Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

**Lecture room ** 1525-103

**Lecture room**

**14h Florian Beyer (Dunedin) Asymptotics and conformal structures of solutions to Einstein’s field equations**

Abstract. Roger Penrose’s idea that the essential information about the asymptotics of solutions of the Einstein’s field equations is contained in the conformal structure and the associated conformal boundary has led to astonishing successes. In his original work, he provided several examples which made the importance of his idea evident. However, the question whether general solutions of Einstein’s field equations are compatible with this proposal remained unanswered. Motived by this, Helmut Friedrich has initiated a research programme to tackle this problem based on his so-called conformal field equations. In this talk I report on the status of this work and some of Friedrich’s results, but also on joint work with collaborators at the University of Otago.

**15h30 Julien Cortier (IHES, Bures-sur-Yvette) On the mass of asymptotically hyperbolic manifolds**

Abstract. By analogy with the ADM mass of asymptotically Euclidean manifolds, a set of global charges can be defined for asymptotically hyperbolic manifolds. We will review their various definitions and , in particular, focus on the notion of “mass aspect” tensor, which gives rise to the energy-momentum vector and arises in the hyperbolic formulation of the positive mass theorem. We will compute these quantities for examples such that the Schwarzschild-anti de Sitter metrics, and we will present a family of counter-examples with “non-positive” mass when completeness is not assumed.