Sur certaines solutions particulières transcendantes des équations d'Einstein
Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliques
On étudie le comportement asymptotique des niveaux d’une fonction temps quasi-concave, définie sur un espace-temps globalement hyperbolique maximal plat de dimension trois, admettant une hypersurface de Cauchy de genre . On donne une réponse positive à une conjecture posée par Benedetti et Guadagnini dans [7]. Plus précisément, on montre que les niveaux d’une telle fonction temps convergent au sens de la topologie de Hausdorff-Gromov équivariante vers un arbre réel. On montre de plus que la limite...
Sur la résolubilité locale des équations d'Einstein
Sur une nouvelle expression de la solution générale des équations d'Einstein avec champ de Maxwell non singulier, aligné, sans source et avec constante cosmologique, en type D
Symmetric space Cartan connections and gravity in three and four dimensions.
Technicalities in the calculation of the 3rd post-Newtonian dynamics
Dynamics of a point-particle system interacting gravitationally according to the general theory of relativity can be analyzed within the canonical formalism of Arnowitt, Deser, and Misner. To describe the property of being a point particle one can employ Dirac delta distribution in the energy-momentum tensor of the system. We report some mathematical difficulties which arise in deriving the 3rd post-Newtonian Hamilton's function for such a system. We also offer ways to overcome partially these difficulties....
Tensorial Euler-Lagrange expressions and conservation laws.
Tensorial Euler-Lagrange expressions and conservation laws. (Short Communication).
Test théorique d'un axiome de la relativité générale
Testing general relativity with pulsar timing.
Tests of gravity using lunar laser ranging.
The Bisognano-Wichmann theorem for charged states and the conformal boundary of a black hole.
The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
The closed Friedman world model with the initial and final singularities as a non-commutative space
The most elegant definition of singularities in general relativity as b-boundary points, when applied to the closed Friedman world model, leads to the disastrous situation: both the initial and final singularities form the single point of the b-boundary which is not Hausdorff separated from the rest of space-time. We apply Alain Connes' method of non-commutative geometry, defined in terms of a C*-algebra, to this case. It turns out that both the initial and final singularities can be analysed as...
The cosmic microwave background.
The cosmological constant.
The global nonlinear stability of the Minkowski space
The graded differential geometry of mixed symmetry tensors
We show how the theory of -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.
The Group of Large Diffeomorphisms in General Relativity
We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
The group structure of supergravity