Maxwell's equations in the Debye potential formalism
Measuring our universe from galaxy redshift surveys.
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...
Metric tensors for homogeneous, isotropic, 5-dimensional pseudo Riemannian models.
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.
Multi-instantons in higher dimensions and superstring solitons.
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.
Netradiční pohled na Lorentzovu transformaci
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...
Non-associative geometry and discrete structure of spacetime
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
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.
Nonlinear Dirac equations.
Non-periodic solutions to relativistic field equations : hyperbolic case