We present recent developments concerning Lorentzian geometry in algebras of generalized functions. These have, in particular, raised a new interest in refined regularity theory for the wave equation on singular space-times.

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

We study the exact construction of D-branes in Lorentzian AdS3. We start by defining a family of conformal field theories that gives a natural Euclidean version of the SL(2,R) CFT and does not correspond to H3 , the analytic continuation of AdS3. We argue that one can recuperate the exact CFT results of Lorentzian AdS3, upon an analytic continuation in the moduli space of these conformal field ...

It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed...

We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature (1, 1). We will investigate the properties of the solutions of these equations and try to relate the conformal invariant dimension of the space of harmonic and twistor spinors to the natural conformal invariants given by the Lorentzian metric. We wil...

The Leech lattice has many strange properties, discovered by Conway, Parker, and Sloane. For example, it has covering radius √ 2, and the orbits of points at distance at least √ 2 from all lattice points correspond to the Niemeier lattices other than the Leech lattice. (See Conway and Sloane [6, Chaps. 22-28].) Most of the properties of the Leech lattice follow from the fact that it is the Dynk...

We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show that if the Dirac current associated with a generic spinor defines a null conformal Killing vector then the spinor must obey a twistor equation with respect ...

In this paper, I discuss whether superluminal particles exist in the general relativistic theory of gravity. It seems that the answer to this question is negative. In truth, the result may only represent a difficulty to special but not general relativity, the later allowing both Lorentzian and Euclidian metrics. An Euclidian metric does not restrict speed. Although only the Lorentzian metric is...