A conventional Stokes description of polarized light is considered in a four-dimensional Lorentzian space, developing a seminal idea of Paul Soleillet [Ann. Phys. (Paris) 12, 23 (1929)]. This provides a striking interpretation for the degree of polarization and the Stokes decomposition of light beams. Malus law and reciprocity theorems for polarizers are studied using this Lorentzian formalism.

It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type ημν = diag (1,−1,−1,−1) this is usually presented as an independent axiom of the theory, which can not be deduced from other assumptions. In this work we show that the above assertion is a consequence of a standard stability analysis of the Einstein equations and nee...

Abstract. In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 2 of the group Γ of positive units of the Lorentzian quadratic form x 1 + · · ·+ x 5 − x 6 . We also show that Γ 2 is a reflection group with respect to a 5-dimensional right-angled convex po...

2+1 gravity for spacetimes with topology R × T has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of tori given by a geodesic in the ”Teichmüller space” of Lorentzian tori. We describe this in detail. We also point out that if the modular group is regarded as...

A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time. For finite lattice ...