Aspects géométriques de la relativité générale - 8 et 9 juin 2010
les exposés auront lieu dans l'amphi 8.

Une affiche est disponible au format PostScript : [] ou PDF : [affiche.pdf]


Mardi 8 juin 2010

Thierry Barbot (Université d'Avignon)
Particles with spin in flat spacetimes

I describe spacetimes of dimension 2+1, locally flat, but containing singular lines corresponding to particles with spin, which are globally hyperbolic. I will prove that this list is complete in the case of stationary spacetimes.
Fichier présentation : [ExposeBarbot.pdf]
Romain Gicquaud (Université de Tours)
Nonlinear stability of the Minkowski spacetime (by H. Lindblad and I. Rodnianski)

I will present the main ideas of the proof of the nonlinear stability of the Minkowski spacetime in harmonic coordinates by H. Lindblad and I. Rodnianski. This proof simplifies the previous proof by D. Christodoulou and S. Klainerman. the main underlying idea is the remark that the Einstein equations in harmonic (wave) coordinates do not satisfy the classical null condition but a natural weaker condition (the weak null condition)
Fichier présentation : [ExposeGicquaud.pdf]
Eric Gourgoulhon (CNRS - Observatoire de Paris)
A geometrical approach to relativistic magnetohydrodynamics

We shall present the advantages of using the tools of differential geometry (Lie derivative, Cartan's exterior calculus) in dealing with general relativistic magnetohydrodynamics (MHD). In particular, we shall recover easily some MHD conservation laws obtained previously with coordinate-based approaches. Applications to black hole and neutron star spacetimes will be discussed.
Fichier présentation : [ExposeGourgoulhon.pdf]

Mercredi 9 Juin 2010

Jean-Philippe Nicolas (Université de Brest)
A conformal approach to asymptotic problems in general relativity

The conformal compactification of Lorentzian manifolds was developed by Roger Penrose in the 1960's. His purpose was to give a local description of asymptotic properties of fields (including the metric) as trace properties of conformally rescaled objects at a boundary of spacetime representing infinity. These ideas lead naturally to a geometrical reformulation and extension of the most prominent analytic theory of asymptotic behaviour: scattering theory. Moreover their use in combination with so-called vector field methods has recently allowed to solve to a large extent the question of the peeling of fields on asymptotically flat spacetimes, which remained unresolved for 40 years. This talk will present the essential principles of Penrose's conformal compactification and of scattering theory, their common features, and the ideas of conformal scattering. The peeling will be discussed briefly in the end if time allows. A large part of the material presented is work in common with Lionel Mason.
Fichier présentation : [ExposeNicolas.pdf]

Xiao Zhang (Chinese Academy of Sciences, Beijing, China)
Asymptotically de Sitter spacetimes and positive mass theorems

Planar coordinates and hyperbolic coordinates are used to separate the de Sitter spacetime into two parts, which give rise to two different spatial infinities. For spacetimes which are asymptotic to either half of the de Sitter spacetime, we are able to provide definitions of the total energy, the total linear momentum, the total angular momentum, respectively. We prove two positive mass theorems, corresponding to these two sorts of spatial infinities, for spacelike hypersurfaces whose mean curvatures are bounded by certain constant from above. This is the joint work with M. Luo and N. Xie.
Fichier présentation : [ExposeZhang.pdf]

Alessandro Nagar (IHÉS)
Interfacing numerical and analytical relativity modelizations of coalescing relativistic binaries: a status report

Currently operating ground-based gravitational wave (GW) detectors LIGO/VIRGO/GEO are currently taking data at the designed sensitivity. Coalescing black-hole binaries and inspiralling neutron star binaries are among the most promising sources of gravitational radiation for these detectors. For the detection to be successful, one needs to know in advance, with sufficient accuracy, the gravitational waveform, so to build accurate "template waveforms" able to extract the signal out of the detector's noise. I will review recent efforts in this direction that are based on the sinergy between numerical relativity calculations, i.e., the numerical solution of Einsten's equations on a supercomputer (in full generality) and analytical calculations based on a suitable resummation of post-Newtonian theory. In particular, this analytical approach, known as the Effective One Body (EOB) approach to the (general relativistic) two-body dynamics, has proven itself successful in: (i) extracting crucial nonperturbative information from numerical relativity waveform data, (ii) to build accurate template waveforms for coalescing black-hole binaries that can be efficiently used for GW data analysis purposes, and (iii) to accurately model also neutron star binaries dynamics and waveforms, thanks to a suitable modelization of tidal effects (theory of relativistic Love numbers).

Éditions précédentes: 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2009Bis, 2010

Ces conférences sont répertoriées dans l'Agenda des Conférences en Mathématiques

Emmanuel Humbert