We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.

The four Rindler quadrants of a pair of oppositely accelerated frames are identified as a (Lorentzian) Mach-Zehnder interferometer. The Rindler frequency dependence of the interference process is expressed by means of a (Lorentzian) differential cross section. The Rindler frequencies of the waves in the two acccelerated frames can be measured directly by means of a simple inertially moving dete...

We consider an asymptotically flat Lorentzian manifold of dimension (1, 3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.

We consider Lorentzian correlation functions in theories with non-relativistic Schrödinger symmetry. We employ the method developed by Skenderis and van Rees in which the contour in complex time defining a given correlation function is associated holographically with the gluing together of Euclidean and Lorentzian patches of spacetimes. This formalism extends appropriately to geometries with Sc...

The asymmetric ABAB-matrix model describes the transfer matrix of threedimensional Lorentzian quantum gravity. We study perturbatively the scaling of the ABAB-matrix model in the neighbourhood of its symmetric solution and deduce the associated renormalization of three-dimensional Lorentzian quantum gravity. pacs: 04.60Gw, 04.20Gz, 04.60Kz, 04.60Nc Presented by J.J. at the Workshop on Random Ge...

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. PACS numbers: 04.20, 02.40 AMS classification scheme numbers: 53C50

This is an informal introduction to stochastic analysis on both Riemanian and Lorentzian manifolds. We review the basics underlying the construction of diffusions on manifolds, highlighting the important differences between the Riemanian and Lorentzian cases. We also discuss a few recent applications which range from biophysics to cosmology.

The asymmetric ABAB-matrix model describes the transfer matrix of threedimensional Lorentzian quantum gravity. We study perturbatively the scaling of the ABAB-matrix model in the neighbourhood of its symmetric solution and deduce the associated renormalization of three-dimensional Lorentzian quantum gravity. pacs: 04.60Gw, 04.20Gz, 04.60Kz, 04.60Nc Presented by J.J. at the Workshop on Random Ge...

We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.