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We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
Causal radial geodesics with a positive interval in the Schwarzschild metric include a subset of trajectories completely confined under a horizon, which compose a thermal statistical ensemble with the Hawking-Gibbons temperature. The…
A spinning particle in the Schwarzschild spacetime deviates from geodesic behavior because of its spin. A spinless particle also deviates from geodesic behavior when a test radiation field is superimposed on the Schwarzschild background: in…
In this article, we look into geodesics in the Schwarzschild-Anti-de Sitter metric in (3+1) spacetime dimensions. We investigate the class of marginally bound geodesics (timelike and null), while comparing their behavior with the normal…
The Doppler shift considered in general relativity involves mixed contributions of distinct, gravitational and kinematical origins and for most metrics or trajectories it takes a complex form. The expression for the Doppler shift may…
In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new…
In this paper we will study the geodesic motion of massive particles, in a Schwarzschild background, with a semi-classical quantum framework called "Polymer Quantum Mechanics" (PQM) in order to investigate the black hole phenomenology…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
In this work we review the classification of geodesics of massive test particles in the gravitational background of the black hole solutions of Einstein-Born-Infeld spacetime. Even though some features are quite similar to those of…
The motion of sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be ``gravitational self-force'' corrections to geodesic motion, analogous to the ``radiation reaction forces''…
By considering a deformation of the Schwarzschild metric in the presence of a minimal measurable length which still respects the equivalence principle, we study corrections to the standard general relativistic predictions for some…
We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to…
In this study, we review some current studies on Gravitational Lensing for black holes, mainly in the context of general relativity. We mainly focus on the analytical studies related to lensing with references to observational results. We…
The complete analytical solutions of the geodesic equation of massive test particles in higher dimensional Schwarzschild, Schwarzschild-(anti)de Sitter, Reissner-Nordstroem and Reissner-Nordstroem-(anti)de Sitter space--times are presented.…
In this paper we prove quantitative results about geodesic approximations to submanifolds in negatively curved spaces. Among the main tools is a new and general Jarn\'{i}k-Besicovitch type theorem in Diophantine approximation. The framework…
We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -- depending on the scalar field's mass -- can be as dense as neutron stars or even…
In this paper, the equations of motion for geodesics in the neutral rotating Black Ring metric are derived and the separability of these equations is considered. The bulk of the paper is concerned with sets of solutions where the geodesic…
In this work a study of the gravity is made using Einstein's equation in the post-Newtonian approach. This is a method to linearise the General Relativity indicated to treat non-relativistic objects. It enables us to construct, from…
A compact object moving on a quasicircular orbit about a Schwarzschild black hole gradually spirals inward due to the dissipative action of its gravitational self-force. But in addition to driving the inspiral, the self-force has a…
In this article, we study the trajectory equations of the bounded radial geodesics in the generalized black-to-white hole bounce with mass difference and the Schwarzschild-to-de Sitter transition approximated by the thin-shell formalism. We…