Charged Test Particles Research Articles

A new kind of Robe’s problem with charged bodies

This paper studies the motion of charged test particle, moving in the outermost layer of a heterogeneous body (taken as first primary) filled with incompressible homogeneous viscous fluid and second primary is taken as point mass, whereas both the primaries are assumed to be charged. We compute the equations of motion of test particle (the third body) and stationary points (circular, axial and out-of-plane stationary points). And also, the stability of stationary points is examined utilizing characteristics equations and Routh–Hurwitz criterion. In addition to this, the numerical analysis of stationary points and their stability are worked out for different values of parameters.

Charged and magnetized particle motion around a static black hole in the Starobinsky–Bel–Robinson gravity

In this work we focus on the effects of Starobinsky–Bel–Robinson (SBR) gravity parameter and external magnetic field on the motion of charged test particles and magnetic dipoles moving around a black hole in the selected gravity theory. We take the external magnetic field to be uniform and aligned along the axis of symmetry. Our results reveal that the effect of the SBR gravity parameter is very strong in the close environment of the central black hole while in the farther distances this effects diminishes very quickly. We see that the effect of the external magnetic field on the particle motion is always dominating over the SBR gravity parameter in farther distances. We show that for the motion of charged test particles the magnetic interaction can mimic the spin up to very rapid rotations for prograde motion of particles, while for the motion of magnetic dipoles magnetic interaction can mimic the spin completely for retrograde motion of such particles. We observe that in both scenarios, the SBR gravity parameter behaves as a weak mimicker of the spin of Kerr black hole. We apply the outcomes of our study to the scenario where a neutron star is assumed to behave as a magnetic dipole moving around the supermassive black hole Sgr A⋆\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^\\star $$\\end{document} to investigate how the magnetic field and the SBR gravity coupling parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} affect the orbits of neutron stars orbiting the supermassive black hole.

Electromagnetic fields with symmetry

We show that if an electromagnetic field is invariant under translations or rotations, three of the six components of the field can be expressed in terms of a (gauge-invariant) scalar potential which is also invariant under these transformations. This scalar potential appears in the constant of motion associated with this symmetry for a charged test particle in this field. We also show that the Cartesian components of the electromagnetic field can be combined to form two SO(2, 1) vectors

Circular motion and collisions of particles with magnetic dipole moment and electric charge in dipolar magnetosphere around Schwarzschild black holes

No-hair theorem indicates that black holes cannot have their own magnetic dipole moment. They can be weakly magnetized in binary systems with a neutron star companion and an accretion disc of charged particles. A simple model suggested by Petterson states that a current loop accreting a Schwarzschild black hole generates dipole-like magnetic fields in the outer region of the loop that are uniform in the inner region. This study considers circular motion and collisions of charged test particles with magnetic dipole moments in the inner and outer regions. First, we derive the effective potential taking into account the magnetic interactions between external magnetic fields with electric charge and the magnetic dipole moment of the particle. We investigate the possible innermost stable circular orbits (ISCOs) of the charged and magnetized particles orbiting the magnetized Schwarzschild black hole inside and outside the current loop. Finally, we explore the collisional processes of these particles near the black hole horizons, examining the effects of magnetic interactions on the critical angular momentum of particles that may collide and the center of mass energy of the colliding particles. We discuss astrophysical relevant objects with magnetic dipole moment and electric charge: magnetized neutron stars, white dwarfs, rotating stellar-mass black holes, electrons, and protons, and also estimate the interaction parameters for them.

Effects of Two Quantum Correction Parameters on Chaotic Dynamics of Particles near Renormalized Group Improved Schwarzschild Black Holes

A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter γ represents the identification of cutoff of the distance scale, and another parameter Ω stems from nonperturbative renormalization group theory. The two parameters are constrained by the data from the shadow of M87* central black hole. The dynamics of electrically charged test particles around the black hole are integrable. However, when the black hole is immersed in an external asymptotically uniform magnetic field, the dynamics are not integrable and may allow for the occurrence of chaos. Employing an explicit symplectic integrator, we survey the contributions of the two parameters to the chaotic dynamical behavior. It is found that a small change of the parameter γ constrained by the shadow of M87* black hole has an almost negligible effect on the dynamical transition of particles from order to chaos. However, a small decrease in the parameter Ω leads to an enhancement in the strength of chaos from the global phase space structure. A theoretical interpretation is given to the different contributions. The term with the parameter Ω dominates the term with the parameter γ, even if the two parameters have same values. In particular, the parameter Ω acts as a repulsive force, and its decrease means a weakening of the repulsive force or equivalently enhancing the attractive force from the black hole. On the other hand, there is a positive Lyapunov exponent that is universally given by the surface gravity of the black hole when Ω≥0 is small and the external magnetic field vanishes. In this case, the horizon would influence chaotic behavior in the motion of charged particles around the black hole surrounded by the external magnetic field. This point can explain why a smaller value of the renormalization group parameter would much easily induce chaos than a larger value.

Charge asymmetric fall under gravity of a plate in general relativity

Charged test particle geodesics determine the fall toward a regular plate whose metric is expressed in plane-symmetric form depending only on the z-direction. Falling conditions are obtained in the test electric/magnetic Maxwell fields for both anisotropic and isotropic plates. These results have implications for particle/antiparticle fall differences in the case of a general relativistic plate.

Periapsis shift in spherically symmetric spacetimes and effects of electric interactions* *This work is partially Supported by the Wuhan University Research Development Fund

The periapsis shift of charged test particles in arbitrary static and spherically symmetric charged spacetimes are studied. Two perturbative methods, the near-circular approximation and post-Newtonian methods, are developed and shown to be very accurate when the results are determined to high orders. The near-circular approximation method is more precise when eccentricity e of the orbit is small, whereas the post-Newtonian method is more effective when orbit semilatus rectum p is large. Results from these two methods are shown to agree when both e is small and p is large. These results are then applied to the Reissner-Nordström spacetime, the Einstein-Maxwell-dilation gravity, and a charged wormhole spacetime. The effects of various parameters on the periapsis shift, particularly that of the electrostatic interaction, are carefully studied. The periapsis shift data of the solar-Mercury are then used to constrain the charges of the Sun and Mercury, and the data of the Sgr A*-S2 periapsis shift are used to determine, for the first time using this method, the constraints of the charges of Sgr A* and S2.

Collisions and dynamics of particles with magnetic dipole moment and electric charge near magnetized rotating Kerr black holes

Analysis of test magnetized and charged particles around black holes immersed in external magnetic fields may help to explain the observed astrophysical phenomena related to black holes, such as the acceleration of particles up to high energies. In this sense, we studied the circular motion of test-charged particles with magnetic dipole orbiting around magnetized rotating Kerr black holes. First, we derive the effective potential for the circular motion of such particles, including interactions between the external magnetic field and the electric charge, and the magnetic interaction between the magnetic dipole. In addition, we analyze the angular momentum and energy of particles corresponding to circular orbits. The effects of magnetic interaction and coupling parameters on the position of innermost stable circular orbits (ISCOs), the energy and angular momentum of the particles at ISCO, and the energy efficiency from the Novikov-Thorne accretion disc have been investigated. We also find cases of degeneracy between magnetic dipole interaction and magnetic coupling parameters, giving the same ISCO radius. Finally, we studied various cases of collisions of neutral, magnetized, and electrically charged particles near rotating Kerr black holes in the presence of external magnetic fields. The critical angular momentum of spinning charged particles is found in which the particles can collide. We also analyze the effects of both magnetic interactions on the center-of-mass energy of the colliding particles.

Charged Particles Moving around a Spherically Symmetric Dilatonic Black Hole

For the static spherically symmetric dilatonic black hole described by the Gibbons–Maeda–Garfinkle–Horowitz–Strominger geometry, we analyze the timelike trajectories for electrically charged test particles. Both cases of an electric black hole and a magnetic one are considered. Finally, we are obtaining the solution to the Klein–Gordon equation in terms of Heun confluent functions and the corresponding energy spectrum. A special attention is given to the role of the dilaton parameter.

Overcharging an accelerating Reissner-Nordström-anti-de Sitter black hole with test field and particle

Accelerating black holes have been widely studied in the context of black hole thermodynamics, holographic gravity theories, and in the description of black holes at the center of galaxies. As a fundamental assumption to ensure spacetime causality, we investigate the weak cosmic censorship conjecture (WCCC) in the accelerating Reissner-Nordström-Anti-de Sitter (RN-AdS) spacetime through the scattering of a charged field and the absorption of a charged particle. For the scattering of a charged scalar field, both near-extremal and extremal accelerating RN-AdS black holes cannot be overcharged, thereby upholding the validity of the WCCC. In the case of the absorption of a test charged particle, the results demonstrate that the event horizon of the extremal accelerating RN-AdS black hole cannot be destroyed, while the event horizon of the near-extremal black hole can be overcharged if the test particle satisfies certain conditions. The above results suggest that, in the case of test particles, second-order effects like self-force and self-energy should be further considered.

Galactic cosmic ray transport in the absence of resonant scattering

ABSTRACT Galactic cosmic ray transport relies on the existence of turbulence on scales comparable with the gyration radius of the particles and with wavenumber vector oriented along the local magnetic field. In the standard picture, in which turbulence is injected at large scales and cascades down to smaller scales, it is all but guaranteed that the turbulent fluctuations at the scales relevant for resonant scattering may be present, either because of anisotropic cascading or because of the onset of damping processes. This raises questions on the nature of cosmic ray scattering, especially at energies ≳1 TeV, where self-generation is hardly relevant. Here, by means of numerical simulations of charged test particles in a prescribed magnetic field, we perform a gedankenexperiment aimed at investigating particle diffusion in a situation in which turbulence is mainly present at large scales, and discuss possible implications of this set-up for cosmic ray transport phenomenology.

First law of black hole thermodynamics and the weak cosmic censorship conjecture for Kerr–Newman Taub–NUT black holes

Stimulated by the recent researches of black hole thermodynamics for black hole with Newman–Unti–Tamburino (NUT) parameter, we investigate the thermodynamics and weak cosmic censorship conjecture for a Kerr–Newman Taub–NUT black hole. By defining the electric charge as a Komar integral over the event horizon, we construct a consistent first law of black hole thermodynamics for a Kerr–Newman Taub–NUT black hole through Euclidean action. Having the first law of black hole thermodynamics, we investigate the weak cosmic censorship conjecture for the black hole with a charged test particle and a complex scalar field. We find that an extremal black hole cannot be destroyed by a charged test particle and a complex scalar field. For a near-extremal black hole with small NUT parameter, it can be destroyed by a charged test particle but cannot be destroyed by a complex scalar field.

Energization of Charged Test Particles in Magnetohydrodynamic Fields: Waves versus Turbulence Picture

Direct numerical simulations of three-dimensional compressible magnetohydrodynamic (MHD) turbulence have been performed in order to study the relation between wave modes and coherent structures and the consequent energization of test particles. Moreover, the question of which is the main mechanism of this particle energization is rigorously discussed. In particular, using the same initial conditions, we analyzed the nonlinear and linear evolution of a turbulent state along with the case of randomized phases. Then, the behaviors of the linear and nonlinear simulations were compared through the study of the time evolution of particle kinetic energy and preferential concentration. Also, spatiotemporal spectra were used to identify the presence of wave modes and quantify the fraction of energy around the MHD modes in linear and nonlinear simulations. Finally, the variation of the correlation time of the external forcing is studied in detail along with the effect on the particle energization (and clustering) and the presence of wave modes. More specifically, particle energization tends to decrease when the fraction of linear energy increases, supporting the idea that energization by structures is the dominant mechanism for particle energization instead of resonance with wave modes as suggested by Fermi energization theory.

Effects of a modified Reissner-Nordström spacetime

A modified Reissner-Nordström spacetime is considered here, where the central object (for example, a black hole or naked singularity) possesses a mass, with an “ordinary”, i.e., Standard Model (SM) electric charge, along with a “dark” electric charge associated with dark matter (DM). The inclusion of this dark charge modifies the gravitational properties of the spacetime, while not affecting ordinary electrodynamics. Geodesic motions of both charged and uncharged SM test particles are modified due to the presence of dark charge. The modifications may allow the detection and measrement of the dark charge. In particular, (1) the effective potential for orbiting particles is modified, and consequently, (2) the angular momenta and ISCOs of test masses in circular orbits are changed from those for the usual Reissner-Nordström case. (3) In the case of a naked singularity, it is possible that a “levitating atmosphere”, due to short distance repulsive gravity, forms at the zero gravity radius, which depends upon both SM and DM charges. A levitating atmosphere may then cloak the naked singularity.

Charged spinning and magnetized test particles orbiting quantum improved charged black holes

In the present work, we aimed to investigate the dynamics of spinning charged and magnetized test particles around both electrically and magnetically charged quantum-improved black holes. We derive the equations of motion for charged spinning test particles using the Mathisson-Papapetrou-Dixon ***equations with the Lorentz coupling term. The radius of innermost stable circular orbits (ISCOs), specific angular momentum, and energy for charged spinless, uncharged spinning, and charged spinning test particles around the charged and non-charged quantum-improved black holes are analyzed separately. We found that the quantum parameter increases the maximum spin value, smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document}, which leads to the nonphysical motion (superluminal motion) of the charged spinning test particle. In contrast, the black hole charge decreases its value. We also found that, in contrast to the Reissner Nordström black hole, spinning charged test particles in the quantum-improved charged black hole have higher smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document}; moreover, positively charged spinning particles can have higher values of smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document} near the extreme black hole cases when compared with uncharged spinning particles. Finally, we investigate the magnetized test particle’s dynamics in the spacetime of a quantum-improved magnetically charged black hole in Quantum Einstein Gravity using the Hamilton–Jacobi equation. We show that the presence of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} increases the maximum value of the effective potential and decreases the minimum energy and angular momentum of magnetized particles at their circular orbits. We found an upper constraint in the black hole charge at the ISCO.

Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions

Metric components of potentials of admissible electromagnetic fields in spaces with simply transitive motion group G4 are found. The components of vector tetrads corresponding to the components of the metric tensors found by Petrov are given. The results obtained complement the coordinate-free classification given in Magazev et al. [Theor. Math. Phys. 156, 1127–1141 (2008)]. Previously, admissible electromagnetic fields were found for the case when three- and four-parameter groups of motions act on hypersurfaces of spacetime. Thus, non-equivalent sets of potentials for all electromagnetic fields that admit three- and four-parameter groups of motions are known now.

Charged particles and quasiperiodic oscillations around magnetized Schwarzschild black holes

We study the motion of charged particles around Schwarzschild black holes immersed in external (i) asymptotically uniform, (ii) dipolar, and (iii) parabolic-like magnetic fields. The effect of the different magnetic-field configurations on the position of innermost stable circular orbits (ISCOs) for test-charged particles is analyzed. Furthermore, we investigated frequencies of radial and vertical oscillations of the charged particles along their stable circular orbits together with the Keplerian one. As an astrophysical application, we explore quasiperiodic oscillations (QPOs) observed in microquasars sourced by black hole candidates in the frame of the relativistic precession (RP) model. In order to obtain constraints on the values of the magnetic parameter and black hole mass for the microquasars GRO J1655-40 and GRS 1915-105, we use the method so-called chi ^2 in the Bayesian approach. Also, we get constraints on the magnetic field around the black hole in the microquasars by treating electrons and protons as oscillating test-charged particles in the accretion disc. Our performed analyses show that the masses of black hole candidates in the above-mentioned objects and magnetic parameters are different for the uniform and dipolar magnetic field configurations. However, no constraints on the magnetic field and black hole masses are obtained in the case of a parabolic magnetic field configuration. The obtained results on the black hole masses are compared with the measurements in independent astrophysical observations of these black hole masses.

Charged test particle scattering and effective one-body metrics with spin

Charged test particle scattering and effective one-body metrics with spin

Circular motion and chaos bound of a charged particle near charged 4D Einstein–Gauss–Bonnet-AdS black holes

The circular motion and chaos bound of one charged particle near 4D charged AdS black holes in the Einstein–Gauss–Bonnet gravity theory are analytically investigated. With the help of the Jacobian matrix, we construct the actual formula of the Lyapunov exponent for the charged particle, which satisfies the upper bound when it is localized at the event horizon. Further considering the Lyapunov exponent in the vicinity of the horizon and studying the 4D charged Einstein–Gauss–Bonnet-AdS black hole with different Gauss–Bonnet coupling coefficients, it is found that it has some specific values to determine whether a violation of chaos bound. The Lyapunov exponent for the circular motion of charged test particle is larger than the static equilibrium because of the appearance of angular momentum. We find that, with the increase of the Gauss–Bonnet coupling coefficient, the black hole gets closer to the extremal state and the bound is more easily violated. For various Gauss–Bonnet coupling coefficients, we obtain a corresponding range of the particle charge, in which the chaos bound is violated. Our results indicate that, as the Gauss–Bonnet coupling coefficient increases, the value of the particle charge violating the chaos bound is even smaller.

Charged particles and Penrose process near charged black holes in Einstein–Maxwell-scalar theory

We study the dynamics of charged test particles around an electrically charged black hole in Einstein–Maxwell-scalar (EMS) gravity. The event horizon properties of the spacetime around the black hole are explored and the upper limit for the EMS theory parameters corresponding to extreme charge and minimal value of the event horizon are found. The effective potential for the radial motion of the charged particles at the equatorial plane is investigated. Specific energy and angular momentum of the particles corresponding to circular stable orbits are also studied. We also investigate the effects of the EMS parameter and the black hole charge on innermost stable circular orbits (ISCOs). We also investigate synchrotron radiation of charged particles in the spacetime of the charged black hole in EMS gravity. We also explore electric Penrose and Bañados–Silk–West processes near the black hole horizon, where we analyse in detail the effects of EMS parameters on energy efficiency in the Penrose process and critical angular momentum that allows colliding particles near the horizon, together with the center of mass energy in charged particles collisions.