Mathematical general relativity, compressible fluids, and more

___________________________________________________________________________________________________________________________________________

Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

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

Thursday Nov. 24, 2011

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

Lecture room 15-25 326 (third floor)

14h   Paul Laurain (Paris 7)  Surfaces with constant mean curvature in a Riemannian manifold of  dimension 3

Abstract.  The surfaces with constant mean curvature (CMC) in a spacelike hypersurface are geometrically and physically very interesting, as shown by Huisken and Yau in 1996 or in the beautiful thesis of Bray. However, the purpose of this talk is not to develop the physical properties of CMC surfaces but to see on an example what are the analytical difficulties encountered when studying these surfaces. In fact, we will  show how to study CMC surfaces in terms of partial differential equations in order to derive geometric properties. We emphasize in particular the key difficulties generated by the conformal invariance of the problem as the phenomena of concentration and we will show how the structure of the equation helps us to overcome them.

15h30  James D.E. Grant (Vienna)  Null injectivity radius estimates

Abstract. I will report on joint work with P.G. LeFloch, in which we use comparison techniques, such as the Rauch comparison theorem and Hessian comparison theorem, to estimate the null injectivity radius on a Lorentzian manifold. This work gives a more geometrical setting for work of Klainerman and Rodnianski on null injectivity radius estimates.

___________________________________________________________________________________________________________________________________________

Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

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

Thursday November 3, 2011

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

Lecture room 15-25 326 (third floor)

14h   Charles Boubel (Strasbourg) Germs of Lorentzian metrics and holonomy

Abstract.  The holonomy group of a pseudo-Riemannian metric g -so e.g. a Riemannian or a Lorentzian metric- is a subgroup of O(g) which indicates, in a certain sense, how much its Levi-Civita connection fails to be flat. A central task related to those groupes is to determine the list of the subgroups of O(g) arising as holonomy, and for each item, to parametrize the set of corresponding metrics and build global examples (i.e. complete or compact). In the Riemannian case, this work is now done. We will see that, regarding holonomy matters, Lorentzian metrics behave totally differenly from Riemannian ones. I will review works of L. Bérard-Bergery, A. Ikemakhen, T. Leistner, A. Galaev, and myself, that together deal with the local aspect of the question.

15h30  David Parlongue (Nice) Breakdown criteria and extendibility in general relativity

Abstract. We will begin this talk by reviewing a geometric breakdown criterion for Einstein’s vacuum equations introduced by S. Klainerman and I. Rodnianski and various improvements (non-vacuum case, integral conditions, various gauge choices). We will then examine a spacetime localization of these criteria. We will focus on consequences in terms of formation of singularities, extendibility of spacetimes, and local regularity of foliations.

___________________________________________________________________________________________________________________________________________

Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

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

Thursday September 29, 2011

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

Lecture room 15-25 1-01 (first floor)

14h  Robert Beig (Vienna) Elastic perturbations of static perfect fluid bodies: Newtonian theory

Abstract.  We describe a model for static self-gravitating bodies with both fluid and elastic properties. This should allow for a rigorous existence theory of solutions near a perfect fluid configuration, e.g. ‘putting mountains on a neutron star’.

15h30 Jacques Smulevici (Orsay) Wave equations on asymptotically AdS black hole 

Abstract. This is joint work with Gustav Holzelgel.  We prove a logarithmic decay estimate for solutions of the linear wave equation on a slowly rotating Kerr-Anti-de-Sitter spacetime. This estimate is expected to be sharp in view of heuristics and numerics from the physics litterature. The underlying reason for the slow decay rate established here can be traced back to a stable trapping phenomenon for asymptotically anti de Sitter black holes near infinity.

___________________________________________________________________________________________________________________________________________

Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

Monday June 13, 2011

Institut Henri Poincaré, Paris, Lecture room 314

11h  Lars Andersson (Potsdam) Linear fields on Kerr spacetime   

Abstract. The problem of nonlinear stability for the Kerr model of a rotating black hole is one of the central problems in general relativity.  The analysis of linear fields of spin 0, 1, 2, on the Kerr spacetime is an important model problem for full nonlinear stability. I will report on recent progress on this problem.

14h  Yvonne Choquet-Bruhat (IHES, Bures-sur-Yvette)  Positive gravitational energy in arbitrary dimensions

Abstract. The most elegant and convincing proof of the positive energy theorem is based on spinors, as did Witten in dimension 3 +1, inspired by heuristic work by Deser and Grisaru originating from supergravity. Our aim here  is to present a streamlined and complete proof, that is valid in arbitrary space dimension and uses only spinors on an oriented Riemannian space without referring to spacetime spinors.