We prove the existence of at least two timelike non self-intersecting periodic geodesics in compact stationary Lorentzian manifolds and we discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a stationary Lorentzian metric if and only if M admits a smooth circle action without fixed points.

The strong maximum principle is proved to hold for weak (in the sense of support functions) suband super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for C spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.

Gauss–Bonnet formula is used to derive a new and simple theorem of nonexistence of vacuum static nonsingular lorentzian wormholes. We also derive simple proofs for the nonexistence of lorentzian wormhole solutions for some classes of static matter such as, for instance, real scalar fields with a generic potential obeying φV ′(φ) ≥ 0 and massless fermions fields.

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.

We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian signature. The main features of the Euclidean model are preserved in the Lorentzian one. In particular, the boundary Hilbert space matches the one of SU(2) loop quantum gravity. As in the Euclidean case, the model can be obtained from the Lorentzian Barrett-Crane model from a flipping of the Poisson ...

The goal of this paper is to present rigorous mathematical formulations and results for Lorentzian models, introduced in physical papers. Lorentzian models represent two dimensional models, where instead of a two-dimensional lattice one considers an ensemble of triangulations of a cylinder, and natural probability measure (Gibbs family) on this ensemble. It appears that correlation functions of...

If a material vacuum exists, with the properties of a superfluid through which already recognized material moves, then it is capable of acting as a universal reference frame and as an intermediary for the production of particle pairs throughout the universe, which as they cool and recombine, become the source of both high-and low-temperature cosmic background radiation, as observed. Moreover, i...

— This paper is a survey of recent results concerning twistor and Killing spinors on Lorentzian manifolds based on lectures given at CIRM, Luminy, in June 1999, and at ESI, Wien, in October 1999. After some basic facts about twistor spinors we explain a relation between Lorentzian twistor spinors with lightlike Dirac current and the Fefferman spaces of strictly pseudoconvex spin manifolds which...

Background. The evidence exists that radicals are crucial agents necessary for the wound regeneration helping to enhance the repair process. Materials and methods. The lineshape of the electron paramagnetic resonance (EPR) spectra of the burn wounds measured with the low microwave power (2.2 mW) was numerically analyzed. The experimental spectra were fitted by the sum of two and three lines. Re...

In an extension of earlier work we investigate the behaviour of two-dimensional Lorentzian quantum gravity under coupling to a conformal field theory with c > 1. This is done by analyzing numerically a system of eight Ising models (corresponding to c = 4) coupled to dynamically triangulated Lorentzian geometries. It is known that a single Ising model couples weakly to Lorentzian quantum gravity...