Related papers: Parameter Space for Orbits in the Schwarzschild Me…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the…
The Schwarzschild metric giving the space time due to a spherically symmetric object is derived in the background of the Robertson Walker metric. In other words the two metrics are merged. It is found that under certain conditions the…
We describe a special class of ballistic geodesics in Schwarzschild space-time, extending to the horizon in the infinite past and future of observer time, which are characterized by the property that they are in 1-1 correspondence, and…
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…
Some features of the Schwarzschild and Kruskal metric are being discussed under the assumption that the Schwarzschild model can be explained geometrically.
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
In this paper, the consequences of introducing a deformed Snyder-Kepler potential in the Schwarzchild metric are investigated. After this modification, it is obtained a dynamically depending horizon with different penetration radius for…
We discuss properties of a 4-dimensional Schwarzschild black hole in a spacetime where one of the spatial dimensions is compactified. As a result of the compactification the event horizon of the black hole is distorted. We use Weyl…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
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,…
We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form,…
Localization properties for Schr\"odinger means are studied in dimension higher than one.
In this work we comment in more detail on what happens to the parametrized framework first presented by Cardoso et al. when there are departures from the Schwarzschild background metric, as well as possible deviations in the "dynamics". We…
The astrophysical relevance of chaos for a test particle with spin moving in Schwarzschild spacetime was the objective of \cite{Verhaaren10}. Even if the results of the study seem to be qualitatively in agreement with similar works, the…
Schwarzschild's orbit-superposition technique is the most developed and well-tested method available for constraining the detailed mass distributions of equilibrium stellar systems. Here I provide a very short overview of the method and its…
Timelike orbits in curved spacetimes encode intrinsic information about the background geometry and serve as critical probes for investigating gravitational theories and source distributions. In this study, we investigate strictly closed…
General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the…
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…
The scattering of spinning test particles by a Schwarzschild black hole is studied. The motion is described according to the Mathisson-Papapetrou-Dixon model for extended bodies in a given gravitational background field. The equatorial…