The Oscillator Groups,Gλ, are the only solvable, non commutative, simply connected Lie groups to admit a Lorentzian bi-invariant metric. For these groups, we give sufficient conditions for a left-invariant pseudo-Riemannian metric to be complete, we determine the group of isometries, we exhibit a left-invariant affine structure and prove that it is not Lorentzian. As an application, we provide ...

A regular vacuum solution in 5D gravity on the principal bundle with the U (1) structural group is proposed as a 4D wormhole. This solution has two null hypersurfaces where an interchange of the sign of some 5D metric components happens. For a 4D observer living on the base of this principal bundle this is a wormhole with two asymptotically flat Lorentzian (Euclidean) spacetimes connected by a ...

Models describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D = 3 Lorentzian spacetimes with constant curvature. The moduli spaces of trajectories are completely and explicitly determined. Trajectories are Lancret curves including ordinary helices. To get the geometric integration of the solutio...

Abstract: Completing the results achieved in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth D-dimensional Lorentzian manifolds. To this end, it is shown that, in any Lorentzian manifold, a sort of “local Wick rotation” of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinates ar...

I introduce a closeness function between causal Lorentzian geometries of finite volume and arbitrary underlying topology. The construction uses the fact that some information on the manifolds and metrics is encoded in the partial order that the causal structure of each metric induces among points randomly scattered in the corresponding manifold with uniform, finite density according to the volu...

The purpose of the paper is to introduce the notion of generalized recurrent Lorentzian transSasakian manifold and study some of the properties of generalized recurrent and Ricci recurrent Lorentzian Trans-Sasakian manifolds.

In this note a proof is given for global existence and uniqueness of minimal Lorentzian surface maps from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.

It is demonstrated that any two reference frames (RFs), which are uniformly and rectilinearly moving relative to each other, can be adjusted via (possibly anisotropic) rescaling and re-synchronization so that the resulting pair of RFs is Lorentzian; this statement remains true if the word “Lorentzian” is replaced by “Galilean” or “Riemannian”, i.e., if a finite positive value of c is replaced b...

Connes’ functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d’Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almosteverywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwar...