les exposés auront lieu dans l'amphi 8.
|Aspects géométriques de la relativité générale - 8 et 9 juin 2010
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Mardi 8 juin 2010
Thierry Barbot (Université d'Avignon)
- Particles with spin in flat spacetimes
Fichier présentation : [ExposeBarbot.pdf]
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.
Romain Gicquaud (Université de Tours)
- Nonlinear stability of the Minkowski spacetime (by H. Lindblad and I.
Fichier présentation : [ExposeGicquaud.pdf]
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)
Eric Gourgoulhon (CNRS - Observatoire de Paris)
- A geometrical approach to relativistic magnetohydrodynamics
Fichier présentation : [ExposeGourgoulhon.pdf]
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.
Mercredi 9 Juin 2010
Jean-Philippe Nicolas (Université de Brest)
- A conformal approach to asymptotic problems in general relativity
Fichier présentation : [ExposeNicolas.pdf]
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.
Xiao Zhang (Chinese Academy of Sciences, Beijing, China)
Asymptotically de Sitter spacetimes and positive mass theorems
Fichier présentation : [ExposeZhang.pdf]
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.
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
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