L'inégalité de Penrose
Lorentzian geometry in the large
Lorentzian geometry in the large has certain similarities and certain fundamental differences from Riemannian geometry in the large. The Morse index theory for timelike geodesics is quite similar to the corresponding theory for Riemannian manifolds. However, results on completeness for Lorentzian manifolds are quite different from the corresponding results for positive definite manifolds. A generalization of global hyperbolicity known as pseudoconvexity is described. It has important implications...
Lorentz-invariant quantum fields in the space-time tangent bundle.
Maxwell's equations in the Debye potential formalism
Méthodes géométriques dans l’étude des équations d’Einstein
L’étude de l’équation des ondes et de ses perturbations a montré l’importance d’un certain nombre d’objets géométriques, tels que les cônes sortants et rentrants, les champs de Lorentz, des repères isotropes adaptés, etc. Parmi les systèmes d’équations hyperboliques non linéaires, les équations d’Einstein jouent un rôle central ; leur étude a nécessité, dans le cas d’un espace-temps courbe, la construction d’objets analogues à ceux du cas plat, cônes, repères adaptés, etc. La construction de ces...
Minimal surfaces, the Dirac operator and the Penrose inequality
Minkowski asymptotic spaces in general relativity
Mirror symmetry and conformal flatness in general relativity.
Modular theory, non-commutative geometry and quantum gravity.
Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone
It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.
Nature of the central singularity in Szekeres models
The occurrence and nature of the central naked singularity in aspherical Szekeres models is investigated here, and the strength of the singularity is discussed. The implications for the cosmic censorship hypothesis are considered.
New results on de Sitter quantum field theory
New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?
AMS Subj. Classification: 83C15, 83C35In this paper we present an overview of our research that was presented at theMASSEE International Congress on Mathematics MICOM 2009 in Ohrid, Macedonia. We deal with quadratic metric–affine gravity, which is an alternative theory of gravity. We present new vacuum solutions for this theory and an attempt to give their physical interpretation on the basis of comparison with existing classical models. These new explicit vacuum solutions of quadratic metric–affine...
Nonexistence of axially symmetric, stationary solution of Einstein vacuum equation with disconnected symmetric event horizon.
Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
Nonlinear connections and spinor geometry.
Non-periodic solutions to relativistic field equations : hyperbolic case
Non-Riemannian gravitational interactions
Recent developments in theories of non-Riemannian gravitational interactions are outlined. The question of the motion of a fluid in the presence of torsion and metric gradient fields is approached in terms of the divergence of the Einstein tensor associated with a general connection. In the absence of matter the variational equations associated with a broad class of actions involving non-Riemannian fields give rise to an Einstein-Proca system associated with the standard Levi-Civita connection.
Note on Simultaneity and the Eisenstein-Maxwell Field.
Notes on new Finsler metric function.