q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, range 1 < 3, q-functions pass from usual Gaussian form, for close to 1, that a heavy tailed distribution, at 3. The value q=2 corresponds Cauchy-Lorentzian distribution. This behavior q-Gaussian functions could be interesting specifi...

We show that positivity of energy for stationary, asymptotically flat, non-singular domains of outer communications is a simple corollary of the Lorentzian splitting theorem. A milestone in mathematical general relativity is the positive energy theorem [8, 10]. It is somewhat surprising that the standard proofs of this result do not have anything to do with Lorentzian geometry. In this note we ...

&lrm;We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property&lrm;. &lrm;We then consider Einstein-like metrics&lrm;, &lrm;Ricci solitons and homogeneity over these spaces&lrm;&lrm;.

There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a similar suppression of the conformal divergence comes about as the result of a non-trivial path-integral measure. The progress of the last few years has establis...

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.