Mathematical general relativity, compressible fluids, and more

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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

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Monday February 14, 2011

Institut Henri Poincaré

Lecture room 01

 

11h – Qian Wang (IHES & Albert Einstein Institute, Potsdam) Breakdown criterion for Einstein Vacuum equations in CMC gauge

Abstract. I will report my recent work on the geometric criterion for the breakdown of Einstein vacuum space-times with the constant mean curvature (CMC) foliation. In this work, the criterion is formulated in terms of time-integrability of the sup- norms of the second fundamental form and derivatives of the lapse function associated to CMC foliation of the space-time. This result is obtained through deriving uniform lower bound on the null radius of injectivity of the light cones. I will sketch the main idea of the proof.

14h – Piotr Chrusciel (Vienna) On the general relativistic constraint equations

Abstract. I will present some new results with Rafe Mazzeo on the construction of solutions of the constraint equations with cylindrical ends.

 

 

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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

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Monday January 31rst, 2011

Institut Henri Poincaré

Lecture room 314

 

11h   Lydia Bieri (Ann Arbor), Geometry of Spacetimes Solving the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation

Abstract. A major goal of mathematical General Relativity (GR) and astrophysics is to precisely describe and finally observe gravitational radiation, one of the predictions of GR. In order to do so, one has to study the null asymptotical limits of the spacetimes for typical sources. Among the latter we find binary neutron stars and binary black hole mergers. In these processes typically mass and momenta are radiated away in form of gravitational waves. D. Christodoulou showed that every gravitational-wave burst has a nonlinear memory. In this talk, we discuss the null asymptotics for spacetimes solving the Einstein-Maxwell (EM) equations, compute the radiated energy and derive limits at null infinity and compare them with the Einstein vacuum (EV) case. The physical insights are based on geometric-analytic investigations of the solution spacetimes.

14h   Jérémie Szeftel (ENS, Paris) Around the bounded L2 curvature conjecture in general relativity

Abstract. We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation on a curved background, where the metric is a rough solution to the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L2 bounds on the curvature tensor of the metric is a major step towards the proof of the bounded L2 curvature conjecture. This is a joint work with Sergiu Klainerman and Igor Rodnianski.

 

 

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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

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie 4 Place Jussieu, 75258 Paris

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Wednesday January 12, 2011

Building 15/16. Lecture room 309

 

14h00   Pieter Blue (Edinburgh) Decay for the Maxwell field outside a Kerr black hole

15h30   Thierry Barbot (Avignon) Particules dans les espaces-temps à courbure constante