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Seminar on Mathematical General Relativity
Laboratoire Jacques-Louis Lions
Sorbonne Université
Organizers
Cécile Huneau (i) Philippe G. LeFloch (ii)
Jacques Smulevici (ii) Jérémie Szeftel (ii)
(i) Ecole Polytechnique, Palaiseau
(ii) Sorbonne Université, Paris
Academic year 2025–2026
Thursday December 18, 2025
lecture room 15-25-322 (nouvelle salle)
14h Flavio ROSSETTI (L’Aquila)
Strong cosmic censorship for de Sitter black holes
Abstract. We will discuss modern formulations of the strong cosmic censorship conjecture (SCCC) and possible resolutions supported by rigorous non-linear results for the spherically symmetric Einstein-Maxwell-scalar field system. We will show that the presence of a positive cosmological constant suggests a violation of the SCCC at a fundamental level of regularity. Indeed, the blueshift mechanism occurring at the Cauchy horizon can be counter-balanced by the dispersive effects encoded in the exponential Price law along (cosmological) black hole event horizons. On the other hand, we show that, if non-smooth black hole solutions are allowed, then the aforementioned violations are non-generic in a positive co-dimension sense.
15h30 Gemma HOOD (Leipzig)
A scattering construction for nonlinear wave equations on Kerr-Anti de Sitter spacetimes
Abstract. Given the sharp logarithmic decay of linear waves on the Kerr-AdS black hole (Holzegel, Smulevici, 2013), it is expected that the Kerr-AdS spacetime is unstable as a solution of the Einstein vacuum equations. However, the scattering construction presented here for exponentially decaying nonlinear waves on a fixed Kerr-AdS background serves as a first step to confronting the scattering problem for the full Einstein system. In this context, one may hope to derive a class of perturbations of Kerr-AdS which remain ‘close’ and dissipate sufficiently fast.
Thursday November 27, 2025
lecture room 15-25-101 (Jussieu)
14h Mahdi HAGHSHENAS (Imperial College, London)
Boundedness and decay of waves on decelerated FLRW spacetimes
Abstract. After outlining the stability problem for Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes, we study the wave equation —as a proxy for the Einstein equations— on decelerated FLRW spacetimes with non-compact, flat spatial sections. We demonstrate how dispersion and expansion affect the long-time behavior of waves. In particular, we present uniform energy bounds and integrated local energy decay estimates across the full decelerated expansion range. Furthermore, we describe a hierarchy of r-weighted energy estimates, in the spirit of the Dafermos–Rodnianski method, which lead to energy decay estimates.
15h30 Pau FIGUERAS (Queen Mary, London)
The initial value problem for higher derivative theories of gravity
Abstract. General relativity can be thought of as a low energy (classical) effective field theory (EFT) of gravity. As such, on general grounds, it is expected that it should receive higher derivative corrections. However, the equations of motion of such higher derivative theories are higher than second order; in particular, they have more than two time derivatives and hence they are plagued with runaway solutions that are unphysical. Furthermore, being higher than second order, it is not clear how to formulate the initial value problem and thus extract their predictions consistently with the EFT expansion. In this talk, I will review the various approaches to this old problem and I will present our recent proposal called “regularization”. As I will show, regularisation allows to formulate the initial value problem for a very general class of higher derivative theories in a manifestly well-posed way, it is covariant and it does not require any fine tuning.
Thursday October 16, 2025
lecture room 15-16-309 (Jussieu)
14h Ludovic SOUETRE (Sorbonne)
Geometric reflective boundary conditions for asymptotically Anti-de Sitter spaces
Abstract. Modeled on the Anti-de Sitter space, asymptotically Anti-de Sitter spaces are defined as Lorentzian manifolds that possess a timelike conformal boundary. As a result, they are not globally hyperbolic. In order to find such spaces that also solve the Einstein equations (with a negative cosmological constant), it is therefore necessary to consider the Cauchy problem as an initial boundary value problem. In this talk, I will discuss the geometric boundary conditions that can be prescribed on the conformal boundary to ensure local existence and uniqueness of solutions in dimension 4. The first one, introduced by Friedrich in his pioneering 1995 work, consists in imposing the boundary conformal class and is known as the Dirichlet boundary condition. The second is a new family of geometric reflective boundary conditions involving both the boundary conformal class and the boundary stress-energy tensor. It can be regarded as the homogeneous Robin boundary conditions.
15h30 Taoran HE (IHES)
Abstract. I will present our recent work on the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system in 1+3 dimensions. This system incorporates gravity, electromagnetic, weak and strong interactions for the initial stage of our universe. The inclusion of the Vlasov field introduces several new challenges. By observing detailed mathematical structures and designing new delicate arguments, we identify a new strong sub-critical regime and prove the nonlinear stability with Kasner exponents lying in this entire regime. Our results extend the work of Fournodavlos, Rodnianski, and Speck from the Einstein-scalar field system to the physically more complex system with the Vlasov field. This is joint work with Xinliang An and Dawei Shen.
Mathematical general relativity, compressible fluids, and more 