Related papers: Bilocal geodesic operators in static spherically-s…
We study spinoptics equations in the Schwarzschild spacetime. We demonstrate that using the explicit and hidden symmetries of this metric one can explicitly solve the equations for complex null tetrad associated with null rays representing…
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend…
It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function $f(\phi)$ and potential $U(\phi)$. The scalar…
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 consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…
I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE…
Solutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional space solutions of geodesic deviation…
An analitical approximation of $<\phi^2>$ for a massive scalar field in a zero temperature vacuum state in static spherically symmetric spacetimes is obtained. The calculations are based on the method for computing vacuum expectations…
We study photon orbits in the background of $(1+3)$-dimensional static, spherically symmetric geometries. In particular, we have obtained exact analytical solutions to the null geodesic equations for light rays in terms of the…
We study the particular case in which Extended Geometric Deformation does consists of consecutive deformations of temporal and spatial components of the metric, in Schwarzschild-like and isotropic coordinates. In the latter, we present two…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
We developed realistic fully general relativistic computer code for simulation of optical projection in a strong, spherically symmetric gravitational field. Standard theoretical analysis of optical projection for an observer in the vicinity…
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…
Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schr\"odinger equation. A simple interconnection between the scattering…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007), and gr-qc/0607001] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general relativistic…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the…
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…