Motion Of Charged Test Particles Research Articles

Particle motion around black hole in Hořava-Lifshitz gravity

Analytical solutions of Maxwell equations around black hole immersed in external uniform magnetic field in the background of the Kehagias-Sfetsos (KS) asymptotically flat black hole solution of Ho\v{r}ava-Lifshitz gravity have been found. Influence of magnetic field on effective potential of the radial motion of charged test particle around black hole immersed in external magnetic field in Ho\v{r}ava-Lifshitz gravity has been investigated by using Hamilton-Jacobi method. Exact analytical solution for dependence of the minimal radius of the circular orbits $r_{\rm mc}$ from KS parameter $\omega$ for motion of test particle around spherical symmetric black hole in Ho\v{r}ava-Lifshitz gravity has been derived. The critical values of the particle's angular momentum for captured particles by black hole in Ho\v{r}ava-Lifshitz gravity have been obtained numerically. The comparison of the obtained numerical results with the astrophysical observational data on radii of the innermost stable circular orbits gives us the estimation of the parameter as $\omega \simeq 3.6 \cdot 10^{-24} {\rm cm}^{-2}$.

Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: Analytical solutions

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr\"om space-time in terms of the Weierstra\ss{} $\ensuremath{\wp}$, $\ensuremath{\sigma}$, and $\ensuremath{\zeta}$ elliptic functions. Based on the study of the polynomials in the $\ensuremath{\vartheta}$ and $r$ equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstr\"om space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstr\"om space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

On the widespread use of the Corrsin hypothesis in diffusion theories

In the past four decades, several nonlinear theories have been developed to describe (i) the motion of charged test particles through a turbulent magnetized plasma and (ii) the random walk of magnetic field lines. In many such theories, the so-called Corrsin independence hypothesis has been applied to enforce analytical tractability. In this note, it is shown that the Corrsin hypothesis is part of most nonlinear diffusion theories. In some cases, the Corrsin approximation is somewhat hidden, while in other cases a different name is used for the same approach. It is shown that even the researchers who criticized the application of this hypothesis have used it in their nonlinear diffusion theories. It is hoped that the present article will eliminate the recently caused confusion about the applicability and validity of the Corrsin hypothesis.

Test particle motion around a black hole in a braneworld

Analytical solutions of Maxwell equations in background spacetime of black hole in braneworld immersed in external uniform magnetic field have been found. Influence of both magnetic and brane parameters on effective potential of the radial motion of charged test particle around slowly rotating black hole in braneworld immersed in uniform magnetic field has been investigated by using Hamilton-Jacobi method. Exact analytical solution for dependence of the radius of the innermost stable circular orbits (ISCO) $r_{\rm ISCO}$ from brane parameter for motion of test particle around nonrotating isolated black hole in braneworld has been derived. It has been shown that radius $r_{\rm ISCO}$ is monotonically growing with the increase of module of brane tidal charge. Comparison of the predictions on $r_{\rm ISCO}$ of the brane world model and of the observational results of ISCO from relativistic accretion disks around black holes provided upper limit for brane tidal charge $\lesssim 10^9 {\rm cm}^2$.

Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge

The exact solution for the electromagnetic field occuring when the Kerr–Taub–NUT compact object is immersed (i) in an originally uniform magnetic field aligned along the axis of axial symmetry (ii) in dipolar magnetic field generated by current loop has been investigated. Effective potential of motion of charged test particle around Kerr–Taub–NUT gravitational source immersed in magnetic field with different values of external magnetic field and NUT parameter has been also investigated. In both cases presence of NUT parameter and magnetic field shifts stable circular orbits in the direction of the central gravitating object. Finally we find analytical solutions of Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star. The star is considered isolated and in vacuum, with monopolar configuration model for the stellar magnetic field.

Brownian motion of a charged test particle near a reflecting boundary at finite temperature

We discuss the random motion of charged test particles driven by quantum electromagnetic fluctuations at finite temperature in both the unbounded flat space and flat spacetime with a reflecting boundary and calculate the mean squared fluctuations in the velocity and position of the test particle. We show that typically the random motion driven by the quantum fluctuations is one order of magnitude less significant than that driven by thermal noise in the unbounded flat space. However, in the flat space with a reflecting plane boundary, the random motion of quantum origin can become much more significant than that of thermal origin at very low temperature.

Features of a charged rotating spacetime

We present an analysis of motion of charged test particles in a class of Gödel-type rotating spacetimes. The wave equation for a charged scalar field is solved and the allowed frequencies are computed. We show that due to the presence of a background electromagnetic field unbounded trajectories may occur in these acausal spacetimes. The problem of field quantization in the presence of closed timelike curves using the Euclidean approach to quantum field theory is also considered.

A gauge-invariant Hamiltonian description of the motion of charged test particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a (relatively little known) Hamiltonian description of theories derived from second-order Lagrangians is presented. Unlike in the standard approach, the canonical momenta arising here are explicitly gauge-invariant and have a clear physical interpretation. The reduced symplectic form obtained this way is (almost) equivalent to Souriau's form. This approach illustrates a new method of deriving equations of motion from field equations.

Two-point boundary value problems in relativistic dynamics

For gyro systems of relativistic type, we obtain solvability conditions for the two-point boundary value problem. We use the geodesic modeling method, in which the original problem is reduced to studying the existence of isotropic geodesic curves of the Kaluts-O. Klein Lorentz metric joining two fibers of a bundle over the configuration manifold of the system. As an example, we consider problems on the motion of charged test particles in an arbitrary electromagnetic field and in the outer Reissner-Nordstrem space-time in the field of a charged black hole and some external electromagnetic field.

Non averaging description of particle dynamics in random nonuniform electric field

The one-dimensional motion of charged test particle in a random non-uniform electric field is considered. In the limit of large-scale field fluctuations the phase picture is built, which corresponds to separate realizations of particle motions. The existence of three types of particle dynamics realizations is shown. Attention is paid to the fact, that information about some realizations is lost at statistic averaging.

Test-particle motion in Einstein's unified field theory. III. Magnetic monopoles and charged particles.

In a previous paper (paper I), we developed a method for finding the exact equations of structure and motion of multipole test particles in Einstein's unified field theory---the theory of the nonsymmetric field. In that paper we also applied the method and found in Einstein's unified field theory the equations of structure and motion of neutral pole-dipole test particles possessing no electromagnetic multipole moments. In a second paper (paper II), we applied the method and found in Einstein's unified field theory the exact equations of structure and motion of charged test particles possessing no magnetic monopole moments. In the present paper (paper III), we apply the method and find in Einstein's unified field theory the exact equations of structure and motion of charged test particles possessing magnetic monopole moments. It follows from the form of these equations of structure and motion that in general in Einstein's unified field theory a test particle possessing a magnetic monopole moment in a background electromagnetic field must also possess spin.

The motion of charged test particles in general relativity

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.

Test-particle motion in Einstein's unified field theory. II. Charged test particles.

In the preceding paper we developed a method for finding the exact equations of structure and motion of multipole test particles in Einstein's unified field theory---the theory of the nonsymmetric field. The method is also applicable to Einstein's gravitational theory. In the preceding paper we applied the method both in Einstein's unified field theory and in Einstein's gravitational theory and found the equations of structure and motion of neutral pole-dipole test particles possessing no electromagnetic multipole moments. In this paper we apply the method and find the equations of structure and motion of charged test particles in Einstein's unified field theory.

Naked singularities, event horizons, and charged particles

The motion of charged test particles in a Reissner-Nordstr\"om field is investigated. It is shown that naked singularities can be destroyed by shooting in suitably charged test particles to produce an event horizon around the source where none previously existed. It is also shown that existing event horizons cannot be destroyed by bombardment with charged test particles. In this manner existing naked singularities can be destroyed but not created while event horizons can be created but not destroyed. Furthermore, a simple explanation is given for radial test-particle oscillations---a phenomenon with no Newtonian analog.

The Equations of Motion of Charged Test Particles in General Relativity

The Equations of Motion of Charged Test Particles in General Relativity