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The Evolution Problem in General Relativity

Total Cost €


EC-Contrib. €






Project "EPGR" data sheet

The following table provides information about the project.


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


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    SORBONNE UNIVERSITE FR (PARIS) coordinator 1˙455˙000.00


 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.


year authors and title journal last update
List of publications.
2019 Volker Schlue
Optical functions in de Sitter
published pages: , ISSN: , DOI:
2017 Volker Schlue, Hans Lindblad
Scattering from infinity for semilinear models of Einstein\'s equations satisfying the weak null condition
published pages: , ISSN: , DOI:
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:
2019 Olivier Graf, Stefan Czimek
The spacelike-characteristic Cauchy problem of general relativity in low regularity
published pages: , ISSN: , DOI:
2019 Siyuan Ma, Lars Andersson,Thomas Backdahl, Pieter Blue
Stability for linearized gravity on the Kerr spacetime
published pages: , ISSN: , DOI:
2017 Sergiu Klainerman and Jeremie Szeftel
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
published pages: , ISSN: , DOI:
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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