Related papers: Characterizing Planetary Orbits and the Trajectori…
After discussing some subtle issues concerning the computation of deflection angle, a general but simple expression of bending angle of light rays in weak deflection limit has been presented for a general static and spherically symmetric…
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…
From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to…
We derive closed formulas for the mass and spin parameters of a Kerr black hole in terms of a minimal quantity of observational data: the red-/blue-shifts of photons emitted by massive particles (stars) moving on geodesics around the black…
As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric)…
In this research note we introduce a new approximation of photon geodesics in Schwarzschild spacetime which is especially useful to describe highly bent trajectories, for which the angle between the initial emission position and the line of…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
We employ the metric of Schwarzschild space surrounded by quintessential matter to study the trajectories of test masses on the motion of a binary system. The results, which are obtained through the gradually approximate approach, can be…
The Kerr spacetime is one of the most widely known solutions to Einstein's vacuum field equations and is commonly used to describe a black hole with mass $m$ and spin $a$. Astrophysical observations in the electromagnetic spectrum as well…
We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter's constant space ($E$, $L$,…
We investigate the properties of the Schwarzschild black hole geometry involving leading one-loop long-distance quantum effects, which arise within the framework of effective field theories of gravity. Our analysis reveals that geodesic…
An attempt is made to describe the general-relativistic equations of motion for the Schwarzschild geometry in terms of the classical concepts of energy and angular momentum. Using the customary terms the geodesic equations can be viewed in…
The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along…
The Hamilton-Jacobi equation for test particles in the Kerr geometry is separable. Using action-angle variables, we establish several relations between various physical quantities that characterize bound timelike geodesic orbits around a…
The general parametrization of a black-hole spacetime in arbitrary metric theories of gravity includes an infinite set of parameters. It is natural to suppose that essential astrophysically observable quantities, such as quasinormal modes,…
The basic geometry of the Solar System -- the shapes, spacings, and orientations of the planetary orbits -- has long been a subject of fascination as well as inspiration for planet formation theories. For exoplanetary systems, those same…
We propose a quantum experiment to measure with high precision the Schwarzschild space-time parameters of the Earth. The scheme can also be applied to measure distances by taking into account the curvature of the Earth's space-time. As a…
The motion with intersections of relativistic gravitating shells in the Schwarzschild gravitational field of a central body is considered. Formulas are derived for calculating parameters of the shells after intersection via their parameters…
Kerr black holes are among the most intriguing predictions of Einstein's general relativity theory. These rotating massive astrophysical objects drag and intermix their surrounding space and time, deflecting and phase-modifying light…
Higher-order photon rings can be expected to be detected in a more detailed image of the black hole found in future observations. These rings are lensed images of the luminous matter surrounding the black hole and are formed by photons that…