Related papers: Generating New Spacetimes through Zermelo Navigati…
We present a framework for the study of lensing in spherically symmetric spacetimes within the context of f(R) gravity. Equations for the propagation of null geodesics, together with an expression for the bending angle are derived for any…
This paper studies the geodesics connecting two time-like separated boundary points in asymptotically anti-de Sitter (AdS) spacetime. We find that in spherically symmetry Schwarzschild AdS black hole, smooth space-like geodesics can connect…
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…
We study a class of higher dimensional warped Einstein spacetimes with one extra dimension. These were originally identified by Brinkmann as those Einstein spacetimes that can be mapped conformally on other Einstein spacetimes, and have…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
The metric gyro-potential of rotating distributions creates centripetal forces that can override Newtonian attraction on the inner and near-zone orbits. Einstein's geodesics in four metric potentials predict Zeeman-like shifts of Keplerian…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from…
We write the Kerr-Schild tetrads in terms of the flat space-time tetrads and of a (1,1) tensor $S^\lambda_\mu$. This tensor can be considered as a projection operator, since it transforms (i) flat space-time tetrads into non-flat tetrads,…
Recently, a link between Lorentzian and Finslerian Geometries has been carried out, leading to the notion of wind Riemannian structure (WRS), a generalization of Finslerian Randers metrics. Here, we further develop this notion and its…
We use zero angular momentum null geodesics in the Kerr-de Sitter spacetime to transform the metric in a generalised Bondi coordinate system. We write the metric components explicitly. Next, we choose the radial coordinate to be the areal…
We consider circular motion in the NUT (Newman-Unti-Tamburino) space-time. Among other things, we determine the location of circular time-like geodesic orbits, in particular of the innermost stable circular orbit (ISCO) and of the…
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating…
In this paper, we study the geodesic motion in spherically symmetric electro-vacuum Euclidean solutions of the Einstein equation. There are two kinds of such solutions: the Euclidean Reissner-Nordstr\"{o}m (ERN) metrics, and the…
The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic…
A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a…
Uncertainties in the satellite world lines lead to dominant positioning errors. In the present work, using the approach presented in \cite{neu14}, a new analysis of these errors is developed inside a great region surrounding Earth. This…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
In this review, we collect several results for conformally standard stationary spacetimes (SxR,g) obtained in terms of a Finsler metric of Randers type on the orbit manifold S that we call Fermat metric. This metric is obtained by applying…
In this contribution it is shown that various aspects of the concept of residual migration can be utilized for the case that a prestack time or depth migration has been performed for a seismic survey and a new depth is available: The…