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source: Institut Henri Poincaré 2015年10月15日

2015-T3 - Mathematical general relativity - CEB Trimester

COURSE: On The Mathematical Theory of Black Holes

Sergiu Klainerman

Department of Mathematics, Princeton University

COURSE: An Introduction to Self-Gravitating Matter

Philippe LeFloch

Laboratoire Jacques-Louis Lions

Centre National de la Recherche Scientifique & Université Pierre et Marie Curie

8/12/2015 - Sergiu Klainerman - Lecture 6 - On The Mathematical Theory of Black Holes 2:15:40

27/11/2015 - Philippe G LeFloch - Lec. 7 - Nonlinear stability of Minkowski space for massive fields 2:10:33

24/11/2015 - Sergiu Klainerman - Lecture 5 - On The Mathematical Theory of Black Holes 2:10:02

17/11/2015 - Jérémie Szeftel - Remarks on the nonlinear stability of Schwarzschild 55:24

19/11/2015 - Thibault Damour - The Structure of Cosmological Singularities 59:36

17/11/2015 - Qian Wang - Global Existence for the Einstein Equations with Massive Scalar Fields 1:03:41

20/11/2015 - Richard Schoen - Localizing Solutions of the Einstein Equations 1:00:19

19/11/2015 - Gustav Holzegel - The Linear Stability of the Schwarzschild Solution 1:02:00

19/11/2015 - Jacques Smulevici - Dynamics in asymptotically AdS spacetimes 47:28

20/11/2015 - Georges Ellis - The Steps Along The Way Whereby Einstein’s General Theory... 1:06:08

19/11/2015 - Demetrios Christodoulou - The Formulation of the Two-Body Problem in General Relativity 1:12:17

17/11/2015 - Mihalis Dafermos - The stability problem for black holes... 1:00:00

17/11/2015 - Jonathan Luk - Interior of Dynamical Vacuum Black Holes 1:04:53

16/11/2015 - Jean Philippe Uzan - Introduction 3:04

16/11/2015 - Roger Penrose - Palatial Twistor Theory: a Quantum Approach to Classical Space-Time 1:02:30

16/11/2015 - Jean-Pierre Bourguignon - General Relativity and Geometry 1:02:34

16/11/2015 - Robert Wald - Dynamic and Thermodynamic Stability of Black Holes and Black Branes 59:01

13/11/2015 - Philippe G. LeFloch - Lecture 6 - The geometry of weakly regular spacetimes 1:57:32

10/11/2015 - Sergiu Klainerman - Lecture 4 - On The Mathematical Theory of Black Holes 2:07:24

06/11/2015 - Philippe G. LeFloch - Lecture 5 - Self-gravitating fluids with bounded variation 2:09:45

03/11/2015 - Sergiu Klainerman - Lecture 3 - On The Mathematical Theory of Black Holes 2:00:14

30/10/2015 - Philippe G. LeFloch - Lecture 4 - Weakly regular Cauchy developments 1:56:50

23/10/2015 - Philippe G. LeFloch - Lecture 3 - Weak solutions to the Einstein equations 2:06:51

20/10/2015 - Sergiu Klainerman - Lecture 2 - On The Mathematical Theory of Black Holes 2:08:47

16/10/2015 - Philippe G. LeFloch - Lecture 2 - Modified gravity and weakly regular spacetimes 2:07:07

16/10/2015 - Sergiu Klainerman - Lecture 1 - On The Mathematical Theory of Black Holes 2:01:08

9/10/2015 - Philippe G. LeFloch - Lecture 1 - An Introduction to Self-Gravitating Matter 1:58:46

This course offers an introduction to some aspects of the dynamics of self-gravitating matter described by the Einstein equations of general relativity. The notion of "weakly regular spacetime" is introduced and the initial value problem for the Einstein equations is solved when the initial data set has solely weak regularity and enjoys T2 or spherical symmetry. The proposed theory allows for impulsive gravitational waves, as well as shock waves, and despite the presence of such singular waves propagating in the spacetime, its global causal geometry can be analyzed: geodesic completeness, crushing singularity property, formation of trapped surfaces, etc. This course also studies the dynamics of self-gravitating massive fields and provides a proof that Minkowski spacetime is nonlinearly stable in presence of massive fields with sufficiently small mass. A small perturbation of an asymptotically flat, spacelike hypersurface in Minkowski space is proven to disperse toward future timelike directions, so that the spacetime is future geodesically complete.

This course is part of the Trimester Program “Mathematical general relativity” which took place at the Institut Henri Poincaré in order to celebrate the 100th anniversary of general relativity.

See http://philippelefloch.org for further information.

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