## Geometry Seminar - Abstracts

### Talk

Monday 12 March 2018, 16:00-17:00 in HG00.058

**Jérémie Joudioux** (RU)

*Introduction to the stability problem in mathematical relativity*

### Abstract

The stability problem in general relativity is a very active field
of research in the domain of mathematical relativity. It consists of the study
of the mechanism of dispersion of a perturbation near a given solution to the
Einstein equations. This mechanism is known in physics under the name of
gravitational waves. If the full nonlinear stability of Minkowski spacetime,
solution of the vacuum Einstein equations, has been proven at the begin of the
90s, the corresponding question for rotating black holes, the Kerr black
holes, is today still an open question. Furthermore, in the presence of
matter, the stability of flat spacetime remains an open problem for many types
of matter models. The purpose of this talk is to introduce the stability
problem in mathematical relativity as a PDE problem. The Cauchy problem for
the Einstein equations is presented; then the question of the stability of
Minkowski spacetime is addressed, and the basic ideas behind are presented.
Finally, I will give a glimpse at the open problems, such as Kerr stability,
or stability in the presence of matter.

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