Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole’s exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton–Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

Investigation of the convergence of the integration algorithm with the choice of the variable of integration at each step using the example of a Luneberg lens

The paper describes an integration algorithm with a choice of a variable at each step in the numerical construction of ray trajectories in a medium with a given dependence of the permittivityon coordinates. The convergence of the calculations to the exact solution is estimated using the example of the problem of calculating the trajectories of rays in a Luneberg lens. It is shown that with a decrease in the grid step, convergence to the exact solution is observed. Purpose. Assess the convergence to an exact solution of an integration algorithm with a choice of a variable at each step using the example of the problem of calculating ray trajectories in a Luneberg lens. Results. The trajectories of rays incident parallel to the ordinate axis and the trajectories of rays incident at an angle to the ordinate axis are calculated. It is shown that with a decrease in the grid step, convergence of the results to the exact solution is observed. Practical significance. It is shown that an integration algorithm with a choice of a variable at each step provides the construction of ray trajectories with an error in the coordinate not exceeding the grid step for the problem of ray propagation in a Luneberg lens.

Геометрическая оптика во вращающемся диэлектрике

Rotating solid-state homogeneous isotropic dielectric without dispersion in the accompanying rotation of the reference frame turns out to be an inhomogeneous anisotropic medium due to the influence of two competing physical mechanisms: the inhomogeneity of free space caused by rotation and entrainment of light by the moving medium. In a rotating dielectric in the geometric optics approximation the eikonal equation and the corresponding system of ordinary differential equations in characteristic form are obtained. The solutions of the equations with the calculated parameters determined using of the first integrals of the system are pairs "opposite “R-ray trajectories and f - phase trajectories fronts. A formula for the intensity of a light pulse propagating along an arbitrary R-trajectories was obtained. "Oncoming “trajectories of both types do not have common points and are shifted to opposite sides of a straight line between end points. Their structural parameters (minimum distance to the axis of rotation, the length of the arc, the region of determination by the azimuthal coordinate, the optical length, etc.) change under the influence of both physical mechanisms, depending on the speed of rotation. Closed optical paths in the RRF for the relay network and for the two-mirror Fabry-Perot resonator in generating laser can be created using two types of mirrors that are adaptable to the frequency of rotation which normals to the reflecting surfaces must have certain different angles with the ray vectors and wavefronts of radiation arriving at the reflector. The Sagnac effect is a consequence inhomogeneity (deformation) of free space along the azimuthal coordinate, and its value is the result of the competing influence of both physical mechanisms.

First Observation of an X-Ray Beam Following a New Geodesic When Gravitational Waves Deform Space-Time

By using X-rays of a linear accelerator (LINAC Siemens X rays, 6 MeV) for medical use, we were able to measure gravitational waves, GW, (amplitude = 56:385mm, frequency =1 = 3Hz, velocity = c and polarization) and its threedimensional effect on X-ray trajectories. The collimated X-ray beam, which is in the plane (X; Y); travels on the Z axis at the speed of light in air and passing through the machine isocenter, until it reaches the target and, ultimate, is recorded in a radiographic film. Apparently, there is an exceptional coincidence in the operation of LINAC and the presence of GW. This coincidence occurred in VIRGINIA, GPS (38.634 351 1, -77.282 523 9), UTC (12/06/2011: 12: 56: 01). This important event, but not sui generis, was recorded in the LINAC computer system, on a film for radiography, in the log file of the cancer treatment center and it was reported to SIEMENS in order to try to find an explanation of a possible hardware failure, some abnormality or any software issue. The physicist and Siemens service engineer on site concluded that such event should never happened because LINAC was not malfunctioning. Consequently, for the X-rays, there was a deviation of the isocenter of the LINAC (△X = (11:5 ± 0:5)mm, △Y = (48 ± 0:5)mm), by the action of the amplitude of GW. The tolerance of a LINAC is lower than these measurements, and the equipment will stop working if they are greater than ±1:0mm for isocenter (zero position) and ±2:0mm for other collimator leaf positions. Therefore, this constitutes a register of space-time alteration with a consequent variation of the path of the X-ray beam. Finally, the registered gravitational waves leave invariant the angle between the axes (X; Y), of the X-ray beam, indicating a constant polarization.

Comparison and Time Evolution of the Geomagnetic Cutoff at the ISS Position: Internal vs External Earth’s Magnetic Field Models

Our back-tracing code (GeoMagSphere) reconstructs the cosmic ray trajectories inside the Earth’s magnetosphere. GeoMagSphere gets the incoming directions of particles entering the magnetopause and disentangles primary from secondary particles (produced in atmosphere) or even particles trapped inside the Earth’s magnetic field. The separation of these particle families allows us to evaluate the geomagnetic rigidity cutoff. The model can be used considering the internal symmetric (IGRF-12) magnetic field only, or adding the asymmetric external one (Tsyganenko models: T89, T96 or TS05). A quantitative comparison among these models is presented for quiet (solar pressure Pdyn < 4 nPa) and disturbed (Pdyn > 4 nPa) periods of solar activity, as well as during solar events like flares, CMEs. In this analysis we focused our attention on magnetic field data in magnetosphere, from Cluster, and simulated cosmic rays for a generic detector on the ISS as for example AMS-02. We found that high solar activity periods, like a large fraction of the period covering years 2011-2015, are better described using IGRF+TS05 model. Results, i.e. the average vertical rigidity cutoff at the ISS orbit, are shown in geographic maps of 2° × 2° cells.