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## Seminar on** **

**Mathematical General Relativity**

*Organizers:** *

* *S. Klainerman *(Princeton)*

#### P.G. LeFloch *(Paris)*

*A. Zeghib (Lyon)*

**Fondations des Sciences Mathématiques de Paris**

**ANR Project**

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

**Thursday May 31, 2012**

### Laboratoire J-L Lions

### Université Pierre et Marie Curie, Paris

**Lecture room 15-25 104**

**Lecture room 15-25 104**

#### 2 pm **Pieter Blue (Edinburg) **

**Decay for the Maxwell field outside a Kerr black hole**

**Abstract. **This talk will repeat some of the material from last year on the same topic (January 12, 2011) and present some new results. The goal of this talk is to prove uniform energy bounds and Morawetz (integrated decay) estimates. In the exterior of a Kerr black hole, one of the components of the Maxwell system satisfies a wave equation with a complex potential. Trapping and the complex potential interact to provide surprisingly difficult challenges. Pseudodifferential techniques can treat a model problem with both features. However, because of the structure of the original Maxwell system, a new idea suggests classical derivatives alone should be sufficient.

#### 3:30 pm **Jonathan Kommemi (Cambridge) **

**Global structure of spherically symmetric spacetimes**

**Abstract. **At the heart of the (weak and strong) cosmic censorship conjectures is a statement regarding singularity formation in general relativity. Even in spherical symmetry, cosmic censorship seems, at the moment, mathematically intractable. To give a framework in which to address these very difficult problems, we will introduce a notion of spherically symmetric ‘strongly tame’ Einstein-matter models, an example of which is given by Einstein-Maxwell-Klein-Gordon (self-gravitating charged scalar fields). We will demonstrate that for any ‘strongly tame’ model there is an a priori characterization of the spacetime boundary. In particular, for any ‘strongly tame’ Einstein-matter model, a ‘first singularity’ must emanate from a spacetime boundary to which the area-radius r extends continuously to zero.