Related papers: Frenet-Serret formalism for null world lines
Fermi normal coordinates provide a standardized way to describe the effects of gravitation from the point of view of an inertial observer. These coordinates have always been introduced via perturbation expansions and were usually limited to…
Vacuum spacetimes admitting a non-twisting geodetic multiple Weyl aligned null direction (WAND) are analyzed in arbitrary dimension using recently developed higher-dimensional Newman-Penrose (NP) formalism. We determine dependence of the…
We propose a formulation of the Penrose plane wave limit in terms of null Fermi coordinates. This provides a physically intuitive (Fermi coordinates are direct measures of geodesic distance in space-time) and manifestly covariant…
This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
The Dirac's bra-ket formalism is generalized to finite-dimensional vector spaces with indefinite metric in a simple mathematical context similar to thatof the theory of general tensors where, in addition, scalar products are introduced with…
Linear regression is widely used to model relationships between responses and predictors. In modern applications, one encounters data where the responses are non-Euclidean random objects situated in a metric space, paired with Euclidean…
In this short paper, Penrose's famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose's singularity theorem are not satisfied as the space-time is not…
The main goal of this paper is to put on solid mathematical grounds the so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open systems. In particular, we derive the Jauho-Meir-Wingreen formula for the time-dependent…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector field. We prove that for non-geodesic such curves there exists a unique…
The Frenet frame is generally known an orthonormal vector frame for curves. But, it does not always meet the needs of curve characterizations. In this study, with the help of associated curves of any spatial curve we obtained a new…
The aim of this manuscript is to review the studies about de Sitter solution and the null infinity of asymptotically flat and de Sitter space-times. Thus, after introducing the de Sitter space-time, the symmetry group is described. Also…
The motion of massless spinning test particles is investigated using the Newman-Penrose formalism within the Mathisson-Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
We present a geometric description to study the relativistic EPR correlations in curved spacetime background given by the application of the Fermi-Walker transport in the relativistic EPR states and we show that its result has the same…
The analysis of gravitino fields in curved spacetimes is usually carried out using the Newman-Penrose formalism. In this paper we consider a more direct approach with eigenspinor-vectors on spheres, to separate out the angular parts of the…
The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these…
In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelism geometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the…