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Lorentzian geometry in the large

John Beem (1997)

Banach Center Publications

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...

Méthodes géométriques dans l’étude des équations d’Einstein

Serge Alinhac (2003/2004)

Séminaire Bourbaki

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...

Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone

Jacek Wesołowski (2007)

Studia Mathematica

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

Pankaj Joshi, Andrzej Królak (1997)

Banach Center Publications

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 Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

Pasic, Vedad (2010)

Mathematica Balkanica New Series

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-Riemannian gravitational interactions

Robin Tucker, Charles Wang (1997)

Banach Center Publications

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.

Currently displaying 161 – 180 of 377