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We introduce a definition of symmetry generating vector fields on manifolds which are equipped with a first-order reductive Cartan geometry. We apply this definition to a number of physically motivated examples and show that our newly…

Mathematical Physics · Physics 2016-08-23 Manuel Hohmann

Certain well-known spacetimes of general relativity (GR) are generated from the collision of suitable null-sources coupled with gravitational waves. This is a classical process underlying the full nonlinearity of GR that may be considered…

General Relativity and Quantum Cosmology · Physics 2024-02-08 M. Halilsoy , V. Memari

The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…

General Relativity and Quantum Cosmology · Physics 2015-11-26 G. Koekoek , J. W. van Holten

In this paper we construct the Fermi coordinates along any arbitrary line in simple analytical way without use the orthogonal frames and their parallel transport. In this manner we extend the Eddington approach to the construction of the…

General Relativity and Quantum Cosmology · Physics 2020-09-17 V. A. Belinski

Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description of them, which may serve as an introduction to recent…

Differential Geometry · Mathematics 2023-10-25 Miguel Ángel Javaloyes , Enrique Pendás-Recondo , Miguel Sánchez

We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…

General Relativity and Quantum Cosmology · Physics 2025-08-19 Thomas P. Kling , Sophia MacQueen Pooler

We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on $M=\R\times S$ and Randers metrics on $S$. In particular, for…

Differential Geometry · Mathematics 2012-04-12 Erasmo Caponio , Miguel Angel Javaloyes , Miguel Sanchez

We generalize the Zermelo navigation problem and its solution on Riemannian manifolds $(M, h)$ admitting a space dependence of a ship's speed $0<|u(x)|_h\leq1$ in the presence of a perturbation $\tilde{W}$ determined by a strong velocity…

Differential Geometry · Mathematics 2019-03-25 Piotr Kopacz

We formulate the concept of time machine structure for spacetimes exhibiting a compactely constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by A. Ori, we…

General Relativity and Quantum Cosmology · Physics 2012-01-05 Jürgen Dietz , Alexander Dirmeier , Mike Scherfner

We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and…

General Relativity and Quantum Cosmology · Physics 2020-09-22 Carolina Figueiredo , José Natário

The Gibbons-Werner method for calculating deflection angles using the Gauss-Bonnet theorem and optical/Jacobi metric has become widely popular in recent years. Werner extended this method to stationary spacetimes, where the optical/Jacobi…

General Relativity and Quantum Cosmology · Physics 2025-03-18 Zonghai Li

In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are…

General Relativity and Quantum Cosmology · Physics 2015-05-18 P. Delva , U. Kostic , A. Cadez

In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis et al. in Eur Phys J C…

General Relativity and Quantum Cosmology · Physics 2022-12-27 E. Kapsabelis , P. G. Kevrekidis , P. C. Stavrinos , A. Triantafyllopoulos

In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There…

General Relativity and Quantum Cosmology · Physics 2023-11-07 Manuel E. Rodrigues , Henrique A. Vieira

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a $3-$dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions…

General Relativity and Quantum Cosmology · Physics 2024-10-15 Marcos A. Argañaraz , Oscar Lasso Andino

Using the relativistic Fermat's principle, we establish a bridge between stationary-complete manifolds which satisfy the observer-manifold condition and pre-Randers metrics, namely, Randers metrics without any restriction on the one-form.…

Differential Geometry · Mathematics 2019-05-14 Jonatan Herrera , Miguel Ángel Javaloyes

Finsler geometry is just riemannian geometry without the quadratic restriction[1]. In this paper, we study the motion of massive(non-zero rest mass) and massless particles for schwarzschild metric in finsler spacetime in the case of two…

General Relativity and Quantum Cosmology · Physics 2018-01-08 V. Sai sumith Reddy

We construct a unified framework of geometrodynamics based on the Finsler geometry to reveal the relationship between spacetime and dynamics.The Lagrangian of electron in electromagnetic field as the Finsler function gives the Finslerian…

Mathematical Physics · Physics 2026-01-13 Mingwei Zhou , Shi-Dong Liang

Finsler spacetime geometry is a canonical extension of Riemannian spacetime geometry. It is based on a general length measure for curves (which does not necessarily arise from a spacetime metric) and it is used as an effective description…

Differential Geometry · Mathematics 2023-11-29 Nicoleta Voicu , Christian Pfeifer , Samira Cheraghchi

We consider the cosmological evolution in an osculating point Barthel-Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe…

General Relativity and Quantum Cosmology · Physics 2021-08-23 Rattanasak Hama , Tiberiu Harko , Sorin V. Sabau , Shahab Shahidi