We explore the electromagnetic fields around a quasi-Kerr compact object assuming it is immersed in an external asymptotically uniform magnetic field. Using the Wald method, components of the electromagnetic field in orthonormal basis have been obtained. We explore the charged particle motion around deformed Kerr compact objects in the presence of external asymptotically uniform magnetic fields. Using the Hamilton-Jacobi equation, we obtain the effective potential expression for the charged particle surrounding a quasi-Kerr compact object immersed in an external magnetic field. It is also derived the dependence of innermost stable circular orbits (ISCOs) from the magnetic and deformation parameters for charged particles motion around a rotating quasi-Kerr compact object. Comparison with ISCO radius measurements has provided the constraint to the deformation parameter as $ε\gtrsim -0.012$. The center of mass (CM) energy of the colliding particles in several physically interesting cases has been studied.
The dynamics of a charged particle moving around a slowly rotating Kerr black hole in the presence of an external magnetic field is investigated. We are interested to explore the conditions under which the charged particle can escape from the gravitational field of the black hole after colliding with another particle. The escape velocity of the charged particle in the innermost stable circular orbit is calculated. The effective potential and escape velocity of the charged particle with angular momentum in the presence of magnetic field is analyzed. This work serves as an extension of a precedi…
We consider a stationary metric immersed in a uniform magnetic field and determine general expressions for the epicyclic frequencies of charged particles. Applications to the Kerr--Newman black hole is reach of physical consequences and reveals some new effects among which the existence of radially and vertically stable circular orbits in the region enclosed by the event horizon and the so-called {\textquotedblleft innermost\textquotedblright} stable circular orbit in the plane of symmetry.
In this work, taking the QED effect into account, we investigate the shadows of the Kerr black holes immersed in uniform magnetic fields through the numerical backward ray-tracing method. We introduce a dimensionless parameter $Λ$ to characterize the strength of magnetic fields and studied the influence of magnetic fields on the Kerr black hole shadows for various spins of the black holes and inclination angles of the observers. In particular, we find that the photon "hairs" appear near the left edge of the shadow in the presence of magnetic fields. The photon hairs may be served as a signatur…
In continuation of our previous study [Phys. Rev. D 99 (2019) 4, 044012], we investigate the motion of charged particles in the $γ$-metric. We provide some examples of curled trajectories in the equatorial plane and escape trajectories outside the equatorial plane. Finally, we consider harmonic oscillations due to small displacements from stable circular orbits on the equatorial plane and compute the epicyclic frequencies for different values of deformation parameter and magnetic field.
In order to test the role of large-scale magnetic fields in quasiperiodic oscillation phenomena observed in microquasars, we study oscillatory motion of charged particles in vicinity of a Schwarzschild black hole immersed into an external asymptotically uniform magnetic field. We determine the fundamental frequencies of small harmonic oscillations of charged test particles around stable circular orbits in the equatorial plane of a magnetized black hole, and discuss the radial profiles of frequencies of the radial and latitudinal harmonic oscillations in dependence on the mass of the black hole…
This paper investigates the motion and acceleration of a particle that is electrically and magnetically charged, which rotates around a cylindrical black hole in the presence of an external asymptotically uniform magnetic field parallel to the z axis. Basically, the work considers the circular orbits of particles rotating around the central object and studies the dependence of the most internal stable circular orbits (ISCO) on the so-called magnetic coupling parameters, which are responsible for the interaction between the external magnetic field and magnetized and charged particles. It is als…
We study the circular orbits of charged particles around a weakly charged Kerr black hole immersed in a weak, axisymmetric magnetic field. Firstly, we review the circular orbits of neutral particles. We then review the circular orbits of charged particles around a weakly charged Kerr black hole and weakly magnetized Kerr black hole. The case of a weakly magnetized and charged black hole is investigated thereafter. We investigate, in particular, the effect of the electromagnetic forces on the charged particles' innermost stable circular orbits. We examine the conditions for the existence of neg…
We derive again the upper entropy bound for a charged object by employing thermodynamics of the Kerr-Newman black hole linearised with respect to its electric charge
The motion of charged test-particles in the gravitational field of a rotating and electromagnetically charged black hole as described by the Kerr-Newman metric is considered. We completely classify the colatitudinal and radial motion on the extended manifold $-\infty \leq r \leq \infty$, including orbits crossing the horizons or $r=0$. Analytical solutions of the equations of motion in terms of elliptic functions are presented which are valid for all types of orbits.
In this article we study the innermost stable circular orbit (ISCO) of electrically charged particles in the electrically charged Reissner-Nordström spacetime, the Kerr-Newman spacetime and the Kerr-Sen spacetime. We find that the radius of the ISCO increases with an increasing particle-black hole charge product $|qQ|$ in the case of attractive Coulomb interaction $qQ<0$. For repulsive Coulomb interaction, the ISCO radius first decreases to a minimum and then increases again, until it diverges as the charge product approaches one. If the charge $Q$ of the black hole is very small, the minimum …
In this work, we consider a rotating charged black hole surrounded by perfect fluid dark matter. We consider the system to be immersed in non-magnetised, pressureless plasma. First, we evaluate the null geodesics in order to study the co-rotating and counter rotating photon orbits. Further, we analyse the null geodesics to calculate the celestial coordinates ($α, β$). The celestial coordinates are used to determine the black hole shadow radius ($R_s$). Thereafter, we observe and analyse the effects of black hole spacetime, perfect fluid dark matter and plasma parameters ($a$, $Q$, $χ$, $k$) on…
We study the dynamics and escape of charged particles initially orbiting a weakly magnetized Kerr black hole after they get kicked in the direction normal to the orbit. The case of neutral particles is analysed first and the escape conditions are given analytically. A general analysis of charged particles innermost stable circular orbits (ISCO)s is performed numerically. We then study the charged particles three-dimensional motion and give an effective condition for their escape. We also discuss how the black hole rotation affects the escape of charged particles and the chaoticness in their dy…
In this study, we consider charged massive scalar fields around a Kerr-Sen spacetime. The radial and angular parts of the covariant Klein-Gordon equation are solved in terms of the confluent Heun function. From the exact radial solution, we obtain the Hawking radiation spectrum and discuss its resonant frequencies. The massless case of the resonant frequencies is also examined.
We perform a comprehensive analysis of the spectrum of proper oscillations (quasinormal modes), transmission/reflection coefficients and Hawking radiation for a massive charged scalar field in the background of the Kerr-Newman black hole immersed in an asymptotically homogeneous magnetic field. There are two main effects: the Zeeman shift of the particle energy in the magnetic field and the difference of values of an electromagnetic potential between the horizon and infinity, i.e. the Faraday induction. We have shown that "turning on" the magnetic field induces a stronger energy-emission rate …
It is reported that Kerr-Newman and Kerr-Sen black holes are unstable to perturbations of charged massive scalar field. In this paper, we study analytically the complex frequencies which characterize charged massive scalar fields in a near-extremal Kerr-Sen black hole. For near-extremal Kerr-Sen black holes and for charged massive scalar fields in the eikonal large-mass $\mathcal{M}\gg μ$ regime, where $\mathcal{M}$ is the mass of the black hole, and $μ$ is the mass of the charged scalar field, we have obtained a simple expression for the dimensionless ratio $ω_I /\left(ω_R - ω_c\right)$, wher…
In this paper, we investigate the dynamics of particles in the background of non-rotating Konoplya and Zhidenko black hole that is immersed in an external uniform magnetic field. The work involves circular motion of electric and magnetic particles and particle acceleration. First the motion of electric charged particles is considered. The effective potential, energy and angular momentum expressions are obtained along with their graphs. The analysis of ISCO shows that radii of ISCO decrease with magnetic interaction parameter. Motion of magnetically charged particles has also been studied.
Photon rings and shadows of Kerr black holes immersed in a swirling universe
Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；Institut für Physik, Carl-von-Ossietzky Universität Oldenburg（奥尔登堡卡尔·冯·奥西茨基大学物理研究所）；Department of Mathematics, University College London（伦敦大学学院数学系）；Departamento de Matemática da Universidade de Aveiro and Center for Research and Development in Mathematics and Applications (CIDMA)（阿威罗大学数学系及数学与应用研发中心）
We consider the propagation of a generic scalar field around a rotating and charged black hole. Using the partial wave method, we find, numerically, the total and partial absorption cross sections for different incidence angles. We investigate the low- and high-frequency limits, finding semi-analytical approximations for the absorption cross section, which we compare with our numerical results. Finally, we consider the superradiant regime, showing that, for charged fields, planar waves can be superradiantly scattered.
The superradiant stability of a Kerr-Newman black hole and charged massive scalar perturbation is investigated. We treat the black hole as a background geometry and study the equation of motion of the scalar perturbation. From the radial equation of motion, we derive the effective potential experienced by the scalar perturbation. By a careful analysis of this effective potential, it is found that when the inner and outer horizons of Kerr-Newman black hole satisfy $\frac{r_-}{r_+}\leqslant\frac{1}{3}$ and the charge-to-mass ratios of scalar perturbation and black hole satisfy $ \frac{q}{μ}\frac…
A family of models of counterrotating and rotating relativistic thin discs of infinite extension based on a charged and magnetized Kerr-NUT metric are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. The metric considered has as limiting cases a charged and magnetized Taub-NUT solution and the well known Kerr-Newman solutions. We show that for Kerr-Newman fields the eigenvalues of the energy-momentum tensor of the disc are for all the values of the parameters real quantities so that these discs do not present heat f…
We provide an explicit, closed and compact expression for the Debye superpotential of a circular source. This superpotential is obtained by integrating the Green function of Teukolsky Master Equation (TME). The Debye potential itself is then, for a particular configuration, calculated in the same manner as the $ϕ_0$ field component is calculated from the Green function of the TME -- by convolution of the Green function with sources. This way we provide an exact field of charged ring and circular current on the Kerr background, finalizing thus the work of Linet.
We investigate particle motion in the vicinity of a $4D$ Einstein-Gauss-Bonnet (EGB) black hole immersed in external asymptotically uniform magnetic field. It is well known that magnetic fields can strongly affect charged particle motion in the black hole vicinity due to the Lorenz force. We find that the presence of the Gauss-Bonnet (GB) coupling gives rise to a similar effect, reducing the radius of the innermost stable circular orbit (ISCO) with respect to the purely relativistic Schwarzschild black hole. Further, we consider particle collisions in the black hole vicinity to determine the c…
In this letter, Parikh-Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is extended, and the emission rate of a charged particle tunnelling from the Kerr-Newman black hole is calculated. The emission spectrum takes the same functional form as that of uncharged particles and consists with an underlying unitary theory but deviates from the pure thermal spectrum. Moreover, our calculation indicates that the emission process is treated as a reversible process in the Parikh-Wilczek tunnelling framework, and the information conservation is a natural result of the…
We consider the equatorial circular motion of a test particle of specific charge q/m << 1 in the Kerr-Newman geometry of a rotating charged black hole. We find the particle's conserved energy and conserved projection of the angular momentum on the black hole's axis of rotation as corrections, in leading order of q/m, to the corresponding energy and angular momentum of a neutral particle. We determine the centripetal force acting on the test particle and, consequently, we find a classical pseudo-Newtonian potential with which one can mimic this general relativistic problem.
We investigate the quasibound states of charged massive scalar fields in the Kerr-Newman black hole spacetime by using a new approach recently developed, which uses the polynomial conditions of the Heun functions. We calculate the resonant frequencies related to the spectrum of quasibound states, as well as its corresponding angular and radial wave eigenfunctions. We also analyze the instability of the system. These results are particularized to the cases of Schwarzschild and Kerr black holes. Additionally, we compare our analytical results with the numerical ones known in the literature. Fina…
In this paper, we consider a charged particle moves around a Weakly Magnetized Kerr-Newman black hole. We first study its circular motion with a detailed analysis in the innermost stable circular orbits(ISCO). Then the dynamics of a particle, kicked out from the circular orbit, is also explored. The final states can be characterized into three different types: bound motion, captured by black hole or escape to spatial infinity. The respective trajectories are shown, and are mainly determined by the energy of a particle after a kick and the initial condition, in which we use Basins of attraction…
Using approximate symmetry methods for differential equations we have investigated the exact and approximate symmetries of a Lagrangian for the geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the exact case, it is shown that the symmetry algebra of the Lagrangian is 17 dimensional. This algebra is related to the 15 dimensional Lie algebra of conformal isometries of Minkowski spacetime. First introducing spin angular momentum per unit mass as a small parameter we consider first-order approximate symmetries of the Kerr metric as a first perturbation of the Schwarzschild m…
Light propagation around a Kerr-like black hole immersed in an inhomogeneous anisotropic plasma in Rastall gravity: Analytical solutions to the equations of motion
This work studies jet-like electromagnetic configurations surrounding a slowly-spinning black-hole immersed in a uniformly magnetized force-free plasma. In the first part of this work, we present a family of stationary solutions that are jet-capable. While these solutions all satisfy the force-free equations and the appropriate boundary conditions, our numerical experiments show a unique relaxed state starting from different initial data, and so one member of the family is likely preferred over the others. In the second part of this work, we analyze the perturbations of this family of jet-like…
We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\wp$, $ζ$ and $σ$ functions as well as the Kleinian $σ$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types. This spacetime is also a solution of $f(R)$ gravity with a constant curvature scalar.
We investigate both the intermediate late-time tail and the asymptotic tail behavior of the charged massive Dirac fields in the background of the Kerr-Newman black hole. We find that the intermediate late-time behavior of charged massive Dirac fields is dominated by an inverse power-law decaying tail without any oscillation, which is different from the oscillatory decaying tails of the scalar field. We note that the dumping exponent depends not only on the angular quantum numbers $m$, the separation constant $λ$ and the rotating parameter $a$, but also on the product $seQ$ of the spin weight o…
The so-called BSW effect is an idealised scenario for high-energy test particle collisions in the vicinity of black holes; if the black hole is extremal and one of the particles fine-tuned, the centre-of-mass collision energy can be arbitrarily high. It has been recently shown that the energy of escaping particles produced in this process can also be arbitrarily high in the given approximation, as long as both the black hole and the escaping particles are charged, regardless of how small the black-hole charge might be. We revisit these results and show that they are also compatible with proper…
In this paper, we investigate the deflection of a charged particle moving in the equatorial plane of Kerr-Newman spacetime, focusing on weak field limit. To this end, we use the Jacobi geometry, which can be described in three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and $(n+1)$-dimensional stationtary spacetime picture. Based on Randers data and Gauss-Bonnet theorem, we utilize osculating Riemannian manifold method and the generalized Jacobi metric method to study the deflection angle, respectively. In the $(n+1)$-dimensional spacetime picture, the motion o…
In this paper the problem of gravitational deflection of relativistic charged massive particles in slowly rotating Kerr-Newman black holes is considered. Toward this purpose we have used two methods: Firstly, we have applied the Gauss-Bonnet theorem (GBT) and the optical geometry to evaluate the deflection angle of charged particles. Secondly, we have presented a detailed analysis of the deflection angle by means of the Hamilton-Jacobi equation recovering the same invariant result for the deflection angle in leading order terms. The crucial point behind the first method is to use the correspon…
The explicit solution for a Kerr-Newman black hole immersed in an external magnetic field, sometimes called the Melvin-Kerr-Newman black hole, has been derived by Ernst and Wild in 1976. In this paper, we clarify the first law and Smarr formula for black holes in a magnetic field. We then define the unique mass which is integrable and reduces to the Kerr-Newman mass in the absence of magnetic field. This defines the thermodynamic potentials of the black hole. Quite strikingly, the mass coincides with the standard Christodoulou-Ruffini mass of a black hole as a function of the entropy, angular …
This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein-Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.
We study dynamics of a test charged particle moving in a weakly charged extreme Kerr throat. Dynamical equations of the particle motion are solved in quadratures. We show explicitly that the Killing tensor of the Kerr spacetime becomes reducible in the extreme Kerr throat geometry. Special types of motion of particles and light are discussed.
The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated angular part is an ordinary spheroidal wave equation. General exact solutions in integral forms and in power series expansion as well as several special solutions with physical interest are given for the radial equation in the non-extreme case. In the extreme case, power series solution to the radial equation is briefly studied. Recurrence relations between coef…
Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colours. It is expected, however, that at certain scales new physics, in particular in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, whic…
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 isola…
We analytically study the optical appearance of an isotropically emitter orbiting near the horizon of a near-extremely rotating Kerr-Sen (KS) black hole which is an electrically charged black hole arising in heterotic string theory. We study the influence of the Sen charge on the observational quantities, including the image position, flux and redshift factor. Moreover, we compare the results with those for a near-extremal Kerr-Newman (KN) black hole, which is the charged rotating black hole in general relativity. We find quantitative corrections of the signatures of these charged black holes …
We study the motion of electrically charged particles, magnetic monopoles, and magnetic dipoles around electrically and magnetically charged stringy black holes. From the analysis of the radius of the innermost stable circular orbit (ISCO) of electrically charged particles, we show that the electric charge $Q$ of stringy black holes can mimic well the spin of Kerr black holes; the black hole magnetic charge $Q_m$ can mimic spins up to $a_* \simeq 0.85$ for magnetic dipoles; the magnetic charge parameter $g$ of a magnetic monopole can mimic spins up to $a_* \simeq 0.8$. This is due to the destr…
We revisit the superradiant stability of Kerr-Newman black holes under a charged massive scalar perturbation. We obtain a newly suitable potential which is not singular at the outer horizon when a radial equation is expressed the Schrödinger-type equation in terms of the tortoise coordinate. From the potential analysis, we find a condition for the superradiant stability of Kerr-Newman black holes.
Motivated by the recent work of the hidden conformal symmetry of the Kerr black hole, we investigate the hidden conformal symmetry of a Kerr-Sen black hole and a Kerr-Newman-Kasuya black hole. Our result shows the conformal symmetry is spontaneously broken due to the periodicity of the azimuthal angle. The absorption across section is in consistence with the finite temperature absorption cross section for a 2D CFT. The entropies of the black holes are reproduced by the Cardy formula.
A (charged) rotating black hole may be unstable against a (charged) massive scalar field perturbation due to the existence of superradiance modes. The stability property depends on the parameters of the system. In this paper, the superradiant stable parameter space is studied for the four-dimensional extremal Kerr and Kerr-Newman black holes under massive and charged massive scalar perturbation. For the extremal Kerr case, it is found that when the angular frequency and proper mass of the scalar perturbation satisfy the inequality $ω<μ/\sqrt{3}$, the extremal Kerr black hole and scalar perturb…
We show that using an adequate coordinate transformation the charged regular black hole solution given by Ayon-Beato and Garcia can be put in the Kerr-Schild form. Then we use this metric in Kerr-Schild Cartesian coordinates with a result given by Virbhadra and obtain the energy distribution associated with this.
Generalized Carter & Rüdiger Constants of $\sqrt{\text{Kerr}}$
Mani L. Bhaumik Institute for Theoretical Physics, University of California Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Department of Physics, University of Arkansas（阿肯色大学物理系）
It is shown that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. To that end, we solve analytically the Klein-Gordon wave equation for a stationary charged massive scalar field in the background of a near-extremal Kerr-Newman black hole. In particular, we derive a simple analytical formula which describes the physical properties of these stationary bound-state resonances of the charged massive scalar fields in the Kerr-Newman black-hole spacetime.
