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.

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated. Keywords—Lorentzian 5-space; Frenet-Serret Invariants; Nonnull Curves.

We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature (2, n−2). Derived geometries include Brinkmann spaces, Lorentzian Einstein-Sasaki spaces and certain warped product structures. Exceptional cases with decomposable holonomy o...

Based on the Collins integral, an analytical expression of a general Lorentz-Gauss vortex beam propagating in free space is derived, which allows one to calculate the linear momentum density of a general Lorentz-Gauss vortex beam in free space. The linear momentum density distribution of a general Lorentz-Gauss vortex beam propagating in free space is graphically demonstrated. The xand y-compon...

In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant (Λ) but without matter fields. We have found that the classical solutions of the Euclidean Einstein equations in this model have “quasi-attractors”, i.e., most trajectories on the a-b plane, where a and b are the scale factors of external an...

Atomic Force Microscopy (AFM), a lithographic technique capable of manufacturing nanometer-sized devices, is a promising alternative to modern lithographic methods. Performing physical simulations to replicate the AFM process is not feasible for large surface simulations, therefore a Monte Carlo approach must be considered. Previous research showed that the physical shape of an oxide dot or wir...

The object of the present paper is to study three-dimensional Lorentzian -Sasakian manifolds which are Ricci-semisymmetry, locally symmetric and have -parallel Ricci tensor. An example of a three-dimensional Lorentzian -Sasakian manifold is given which verifies all the Theorems.

We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher-dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.

In this note a proof is given for local existence and uniqueness of minimal surfaces with the topology of the halfplane respectively a cylinder of Lorentzian type with values in certain Lorentzian manifolds for given initial values up to the first derivatives. Global existence is proved for the case that the target manifold is diffeomorphic to Rn.