Related papers: Parameter Space for Orbits in the Schwarzschild Me…
We characterise the octahedrality of Lipschitz-free space norm in terms of a new geometric property of the underlying metric space. We study the metric spaces with and without this property. Quite surprisingly, metric spaces without this…
The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.
Since its first introduction, the Schwarzschild metric has been written in various coordinate systems. This has been done primarily to understand the nature of the coordinate singularity at the event horizon. However, very often, the…
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…
A small deformation controlled by four free parameters to the Schwarzschild metric could be referred to a nonspinning black hole solution in alternative theories of gravity. Because such a non-Schwarzschild metric can be changed into a…
This study investigates the exact geometry of the configuration space in three-dimensional rotational motion planning. A parameterization of configuration space obstacles is derived for a given triangulated or ball-approximated scene with…
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
We show that mass parameter and radial coordinate values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean…
Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one…
We consider physical parameters of Levin and Perez-Giz's `periodic table of orbits' around the Schwarzschild black hole, where each periodic orbit is classified according to three integers $(z,w,v)$. In particular, we chart its distribution…
The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is…
The $n$-time generalization of Schwarzschild solution is considered. The equations of geodesics for the metric are integrated. The multitemporal analogues of Newton laws for the extended objects described by the solution are suggested. The…
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…
We demonstrate that in the case of Schwarzschild spacetime the Doppler shift is partially factorized into terms representing relativistic, kinematical and the gravitational contributions. The condition for the complete factorization is…
The characteristic features were found in the electromagnetic spectrum of radiation from free falling dipole, when it is fall radially into a Schwarzschild black hole. These features can be used as another method for the black hole mass…
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
We study the black hole's shadow for Schwarzschild - de Sitter and Kerr - de Sitter metrics with the contribution of the cosmological constant \Lambda. Based on the reported parameters of the M87* black hole shadow we obtain constraints for…
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…
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…
We consider a model in which accelerated particles experience line--elements with maximal acceleration corrections. When applied to the Schwarzschild metric, the effective field experienced by accelerated test particles contains corrections…