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Seminar at the

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie, Paris

Organizers

 Philippe G. LeFloch (Paris)

 Jacques Smulevici (Orsay)

Jérémie Szeftel (Paris)


Dates of the Seminar for this Fall: 

October 9, November 20, December 4


 

Monday October 9, 2017

room 15/16-309

 14h Daniel Monclair (Orsay)

Attractors in spacetimes and time functions

Abstract.  A time function on a Lorentzian manifold is a continuous real valued function which is increasing along all future directed causal curves. A result of Hawking states that the existence of a time function is equivalent to stable causality, i.e. the impossibility of generating timelike loops even after small perturbations of the metric. We will discuss a construction of time functions which is quite different from Hawking’s construction, in the sense that it produces functions that still have interesting properties for non stably causal spacetimes (while Hawking’s time functions fail to be continuous without stable causality). Our approach is based on a notion of attracting sets in spacetimes, following the work of Conley on Lyapunov functions.

 15h30 The-Cang Nguyen (Paris)

Global dispersion of self-gravitating massive matter in spherical symmetry

Abstract.  We study massive matter fields evolving under their own gravitational field and we generalize results established by Christodoulou for the spherically symmetric evolution of massless scalar fields governed by the Einstein equations. We encompass both Einstein’s theory and the f(R)-theory of modified gravity defined from a generalized Hilbert-Einstein functional depending on a nonlinear function f(R) of the spacetime scalar curvature R. This is a joint work with P.G. LeFloch and F. Mena.


 

Monday November 20, 2017

room 16-26 113

 14h Frederico Pasqualotto (Princeton)

Nonlinear stability for the Maxwell–Born–Infeld system on a Schwarzschild background

Abstract. The Maxwell–Born–Infeld (MBI) theory is a hyperbolic system of PDEs which describes nonlinear electromagnetism. Due to its tensorial and quasilinear nature, this system can be seen as a nonlinear model problem to study the stability properties of solutions to the Einstein vacuum equations. In this talk, I will present a nonlinear stability result for the MBI system on a fixed Schwarzschild background, when the initial data are constrained to be small. A crucial element of the proof is the observation that some null components of the MBI field satisfy “good” Fackerell–Ipser equations, as in the linear Maxwell case. However, in the MBI case, these equations are coupled through cubic nonlinear right hand sides, which contain all components of the MBI field. In order to resolve the coupling, we prove high-order energy decay and, subsequently, pointwise decay for all the components of the MBI field. This is achieved through the application of many ideas developed in recent years, regarding the decay of linear fields.

 15h30 Volker Schlue (Paris)

TBA


 

Monday December 4, 2017

room 16-26 113

 14h Siyuan Ma (Potsdam)

On Maxwell field and linearized gravity in Kerr

Abstract.  I will consider both Maxwell field and linearized gravity on Kerr backgrounds, and present recent results in obtaining energy and Morawetz estimates for the extreme Newman-Penrose components.

 15h30 Claudio Paganini (Potsdam)

The fingerprints of black holes – shadows and their degeneracies

Abstract.  First I will introduce the concept of the shadow of a black hole and what it means for the shadows of two observers to be degenerate. I will then present preliminary results showing that no continuous degenerations exist between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore an observer can, by measuring the black holes shadow, in principle determine the angular momentum and the charge of the black hole under observation, as well as his radial distance from the black hole and his angle of elevation above the equatorial plane.