Related papers: Relativistic Diffusions and Schwarzschild Geometry
The purpose of this note is to introduce and study a relativistic motion whose acceleration, in proper time, is given by a white noise. We begin with the flat case of special relativity, continue with the case of general relativity, and…
We propose a novel linear perturbation scheme to study the stability properties of the stationary transonic integral solutions for axisymmetric matter flow around astrophysical black holes for the Schwarzschild as well as for rotating…
We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of…
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light,…
Motivated by recent achievements of a full general relativistic method in estimating the mass-to-distance ratio of supermassive black holes hosted at the core of active galactic nuclei, we introduce the new concept redshift rapidity in…
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…
We study the conditions under which an analog acoustic geometry of a relativistic fluid in flat spacetime can take the same form as the Schwarzschild black hole geometry. We find that the speed of sound must necessarily be equal to the…
Propagation of relativistic particles in the Schwarzschild gravitational field is studied. Particles emitted radially outward with speed at infinity exceeding c/2^0.5 are observed to be accelerated in the gravitational field by a distant…
The leading-order gravitational time delay of relativistic neutral massive particles (e.g., neutrinos or high-energy cosmic-ray particles) caused by a moving Schwarzschild black hole with a constant radial velocity is investigated for the…
We study the thermodynamics of a moving Schwarzschild black hole, identifying the temperature and entropy in a relativistic scenario. Furthermore, we set arguments in a framework relating invariant geometrical quantities under global…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…
This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation…
In this methodological paper we consider geodesic motion of particles in a spherically symmetric black hole space-times. We develop an approach based on splitting the velocity of a freely falling particle to the flow velocity, which depends…
In this paper we analyze the spacetime geometry due to a Schwarzschild object having uniform accelerated motion. In the beginning, we investigate the gravitational field due to a uniformly moving Schwarzschild object and obtain the…
We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are…
A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced by C. Chevalier and F. Debbasch, both in a heuristic and analytic way. A pathwise approach of these processes is proposed…
For the evolution of a compressible fluid in spherical symmetry on a Schwarzschild curved background, we design a class of well-balanced numerical algorithms with first-order or second-order of accuracy. We treat both the relativistic…
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…