EPGR SIGNED
The Evolution Problem in General Relativity
Total Cost €
0EC-Contrib. €
0Partnership
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Project "EPGR" data sheet
The following table provides information about the project.
| Coordinator |
UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6
There are not information about this coordinator. Please contact Fabio for more information, thanks. |
| Coordinator Country | France [FR] |
| Total cost | 1˙455˙000 € |
| EC max contribution | 1˙455˙000 € (100%) |
| Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
| Code Call | ERC-2016-COG |
| Funding Scheme | ERC-COG |
| Starting year | 2017 |
| Duration (year-month-day) | from 2017-05-01 to 2022-04-30 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | SORBONNE UNIVERSITE | FR (PARIS) | coordinator | 1˙455˙000.00 |
| 2 | UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6 | FR (PARIS) | coordinator | 0.00 |
Map
Project objective
General relativity has been introduced by A. Einstein in 1915. It is a major theory of modern physics and at the same time has led to fascinating mathematical problems. The present proposal focusses on two aspects of the evolution problem for the Einstein equations which has been initiated by the pioneering work of Y. Choquet-Bruhat in 1952.
The Einstein equations form a nonlinear system of partial differential equations of hyperbolic type whose complexity raises significant challenges to its mathematical analysis. The goal of this project is to strengthen our understanding of two important themes concerning the evolution problem in general relativity. On the one hand, the control of low regularity solutions of the Einstein equations, a topic which is intimately linked with the celebrated cosmic censorship conjectures of R. Penrose, a major open problem in the field. On the other hand, the question of the stability of particular solutions of the Einstein equations in the wake of the groundbreaking proof of the stability of the Minkowski space-time due to D. Christodoulou and S. Klainerman. These directions are extremely active and have recently led to impressive results. More specifically, this project proposes to consider the following two work packages
-Going beyond the bounded L2 curvature theorem. This result has been recently obtained by the PI in collaboration with S. Klainerman and I. Rodnianski and is the sharpest result in so far as low regularity solutions of the Einstein equations are concerned. Yet, the fundamental quest towards a scale invariant well-posedness criterion for the Einstein equations remains wide open.
-The black hole stability problem. This problem concerns the stability of the Kerr metrics which form a 2-parameter family of solutions to the Einstein vacuum equations. Many results have been obtained concerning various versions of linear stability, but significant challenges remain in order to tackle the nonlinear stability result.
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2019 |
Volker Schlue Optical functions in de Sitter published pages: , ISSN: , DOI: |
2020-01-29 | |
| 2017 |
Volker Schlue, Hans Lindblad Scattering from infinity for semilinear models of Einstein\'s equations satisfying the weak null condition published pages: , ISSN: , DOI: |
2020-01-29 | |
| 2019 |
Grigorios Fournodavlos, Volker Schlue On “Hard Stars†in General Relativity published pages: 2135-2172, ISSN: 1424-0637, DOI: 10.1007/s00023-019-00793-4 |
Annales Henri Poincaré 20/7 | 2020-01-29 |
| 2019 |
Olivier Graf, Stefan Czimek The canonical foliation on null hypersurfaces in low regularity published pages: , ISSN: , DOI: |
2020-01-29 | |
| 2019 |
Olivier Graf, Stefan Czimek The spacelike-characteristic Cauchy problem of general relativity in low regularity published pages: , ISSN: , DOI: |
2020-01-29 | |
| 2019 |
Siyuan Ma, Lars Andersson,Thomas Backdahl, Pieter Blue Stability for linearized gravity on the Kerr spacetime published pages: , ISSN: , DOI: |
2020-01-29 | |
| 2017 |
Sergiu Klainerman and Jeremie Szeftel Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations published pages: , ISSN: , DOI: |
2020-01-29 | |
| 2018 |
Jeremie Szeftel Parametrix for wave equations on a rough background III: Space-time regularityof the phase published pages: 321 pages, ISSN: 0303-1179, DOI: |
Asterisque 401 | 2019-05-03 |
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