Related papers: Generating New Spacetimes through Zermelo Navigati…
In this paper, we investigate the holonomy structure of the most accessible and demonstrative 2-dimensional Finsler surfaces, the Randers surfaces. Randers metrics can be considered as the solutions of the Zermelo navigation problem. We…
The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and…
The relative geodesic motion on $(1+3)$-dimensional anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for the de Sitter spacetimes. In this approach the…
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main…
We argue that the curvature generated by a gravitational field can be used to calculate the corresponding metric which determines the trajectories of freely falling test particles. To this end, we present a method to compute the metric from…
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A…
In this paper, we study the \texttt{Ehlers' transformation} (sometimes called gravitational duality rotation) for \texttt{reciprocal} static metrics. First we introduce the concept of reciprocal metric. We prove a theorem which shows how we…
We present a new method for finding principal null directions (PNDs). Because our method assumes as input the intrinsic metric and extrinsic curvature of a spacelike hypersurface, it should be particularly useful to numerical relativists.…
Using a metric conformal formulation of the Einstein equations, we develop a construction of 4-dimensional anti-de Sitter-like spacetimes coupled to tracefree matter models. Our strategy relies on the formulation of an initial-boundary…
Tremendous progress has been made recently in modelling the morphology and kinematics of centers of galaxies. Increasingly realistic models are built for central bar, bulge, nucleus and black hole of galaxies, including our own. The newly…
Is it possible to find imprints of a black hole ringdown through gravitational lensing? To address this question, we formulate an analytic description of weak-field and strong-deflection lensing of light in a time-dependent, perturbed…
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic, we construct a family of metrics depending on a small…
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…
Recent observations of the orbits of star clusters around Sgr $A^\star$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up…
This paper uses the Kerr geodesic equations for massless particles to derive an acceleration vector in both Boyer-Lindquist and Cartesian coordinates. As a special case, the Schwarzschild acceleration due to a non-rotating mass has a…
The space of the associative commutative hyper complex numbers, H_4, is a 4-dimensional metric Finsler space with the Berwald-Moor metric. It provides the possibility to construct the tensor fields on the base of the analytical functions of…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
Starting from the Einstein equations in Schwarzschild-de Sitter (SdS) spacetime and imposing Friedmann-Robertson-Walker coordinates at large distances, we find two coordinate systems with time-dependent metrics that are smooth across both…
The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we…