Related papers: Characterizing Planetary Orbits and the Trajectori…
Exact analytic expressions for planetary orbits and light trajectories in the Reissner-Nordstrom geometry are presented. They are characterized in a map specified by three dimensionless parameters for the planetary orbits, while two…
Some features of a parametrized space of orbits in the Schwarzschild geometry are described.
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…
A new parameter space is used to classify circular orbits in the Schwarzschild metric.
Exact analytic expressions for various characteristics of the hyperbolic-type orbits of a particle in the Schwarzschild geometry are presented. A useful simple approximation formula is given for the case when the deviation from the…
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…
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…
This paper investigates the trajectories of light beams in a Kerr metric, which describes the gravitational field in the neighborhood of a rotating black hole. After reduction by cyclic coordinates, this problem reduces to analysis of a…
This paper systematically revisits the critical orbits of test particles moving in various black hole backgrounds, including the Schwarzschild, Reissner-Nordstr\"{o}m, Kerr, and Kerr-Newman spacetimes. We identify the critical orbit cases…
The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…
Phase space method provides a novel way for deducing qualitative features of nonlinear differential equations without actually solving them. The method is applied here for analyzing stability of circular orbits of test particles in various…
The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…
We present a novel orbit parameterization in spherical coordinates. This parameterization enables the mixing of varying and invariant orbital parameters, and clarifies the physics of the orbit. It also simplifies the process of placing…
Since the full General Theory of Relativity has been unveiled to the scientific community in 1915, many solutions to the vacuum Einstein field equations have been found and studied. This paper aims at documenting exhaustively the derivation…
We study the time-like geodesic congruences, in the space-time geometry of a Schwarzschild black hole surrounded by quintessence. The nature of effective potential along with the structure of the possible orbits for test particles in view…
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…
We analyse test particle's trajectories around the geometry of a Schwarzschild black hole. In order to resemble sections of jets in the neighborhood of a black hole, we consider the conserved quantities corresponding to constraints imposed…
Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics…
We propose new analytic formulae describing light bending in Schwarzschild metric. For emission radii above the photon orbit at 1.5 Schwarzschild radius, the formulae have an accuracy of better than 0.2% for the bending angle and 3% for the…
Variability in active galactic nuclei is observed in ultraviolet to X-ray emission based light curves. This could be attributed to orbital signatures of the plasma that constitutes the accretion flow on the putative disk or in the…