Related papers: Is a Circular Orbit Possible According to General …
Some features of a parametrized space of orbits in the Schwarzschild geometry are described.
Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can…
A simple orbit classification constraint extension to stellar dynamical modeling using Schwarzschild's method is demonstrated. The classification scheme used is the existing `orbit circularity' scheme (lambda_z) where orbits are split into…
All possible orbital trajectories and their analytical expressions in the Schwarzschild metric are presented in a single complete map characterized by two dimensionless parameters. While three possible pairs of parameters with different…
We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits,…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
The Mathisson-Papapetrou equations in the Schwarzschild background both at Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic circular orbits of a spinning particle in…
We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented…
We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with…
We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…
We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst…
Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being…
We study geodesics in the Schwarzschild space-time affected by an uncertainty in the mass parameter described by a Gaussian distribution. This study could serve as a first attempt at investigating possible quantum effects of black hole…
An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for…
The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the…
We study the circular orbits of charged particles around a weakly charged Schwarzschild black hole immersed in a weak, axisymmetric magnetic field. We start by reviewing the circular orbits of neutral particles and charged particles around…
We numerically investigate the motion of stars on the meridional plane of an axially symmetric disk galaxy model, containing a central supermassive black hole, represented by the Paczynski-Wiita potential. By using this pseudo-Newtonian…
We investigate the effects of space noncommutativity and the generalized uncertainty principle on the stability of circular orbits of particles in both a central force potential and Schwarzschild spacetime. We find noncommutative form of…
Ultrarelativistic circular orbits of spinning particles in a Schwarzschild field described by the Mathisson-Papapetrou equations are considered. The preliminary estimates of the possible synchrotron electromagnetic radiation of highly…