The exact analytic solutions of the Maxwell equations in the exterior of a boosted rotating black hole immersed in an external magnetic field are obtained. The effect of boost as well as electromagnetic field on charged particle motion and energy extraction process -- magnetic Penrose process around black hole is studied. It justifies however the well known statement that magnetic field greatly increases efficiency of energy extraction which is further boosted by the boost velocity.
The spacetime of a boosted Bondi-Sachs rotating black hole is considered as a proper background to examine electromagnetic configurations connected to analytic solutions of Maxwell equations. In our analysis, we first use the Bondi-Sachs transformations in order to bring the boosted rotating black hole metric into the Kerr-Schild form, from which zero angular momentum observers (ZAMOs) are constructed via the ADM formalism. In Kerr-Schild coordinates we obtain the Killing fields as sources of Maxwell electrodynamics, and we fix a ZAMO in order to evaluate the components of the electric and mag…
We use the overlapping grids method to construct a fourth order accurate discretization of a first order reduction of the Klein-Gordon scalar field equation on a boosted spinning black hole blackground in axisymmetry. This method allows us to use a spherical outer boundary and excise the singularity from the domain with a spheroidal inner boundary which is moving with respect to the main grid. We discuss the use of higher order accurate energy conserving schemes to handle the axis of symmetry and compare it with a simpler technique based on regularity conditions. We also compare the single gri…
We extend the Wald solution to a black hole that is also boosted. More specifically, we derive analytic solutions for the Maxwell equations for a rotating black hole moving at constant speed in an asymptotically uniform magnetic test field. By adopting Kerr-Schild coordinates we avoid singular behaviours at the horizon and obtain a complete description of the charge and current distributions in terms of the black-hole spin and boost. Using this solution, we compute the energy losses expected when charged particles are accelerated along the magnetic field lines, improving previous estimates tha…
We study the collision of two slowly rotating, initially non boosted, black holes in the close limit. A ``punctures'' modification of the Bowen - York method is used to construct conformally flat initial data appropriate to the problem. We keep only the lowest nontrivial orders capable of giving rise to radiation of both gravitational energy and angular momentum. We show that even with these simplifications an extension to higher orders of the linear Regge-Wheeler-Zerilli black hole perturbation theory, is required to deal with the evolution equations of the leading contributing multipoles. Th…
We present a new solution in 5D Einstein-Maxwell-dilaton gravity describing an equilibrium configuration of extremal rotating black holes with lens space horizon topologies. The basic properties of the solution are investigated and the basic physical quantities are calculated. It is shown that the black hole horizons are superconducting in the sense that they expel the magnetic flux lines.
A closed form analytic solution is found for the electromagnetic field of the charged uniformly rotating conducting disk for all values of the tip speed $v$ up to $c$. For $v=c$ it becomes the Magic field of the Kerr-Newman black hole with $G$ set to zero. The field energy, field angular momentum and gyromagnetic ratio are calculated and compared with those of the electron. A new mathematical expression that sums products of 3 Legendre functions each of a different argument, is demonstrated.
We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) tha…
The exact analytical solutions for vacuum electromagnetic fields of slowly rotating magnetized compact stars in conformal gravity have been studied. Taking the realistic dipolar magnetic field configuration for the star, analytical solutions of the Maxwell equations for the near zone magnetic and the electric fields exterior to a slowly rotating magnetized relativistic star in conformal gravity are obtained. In addition, the dipolar electromagnetic radiation and energy losses from the rotating magnetized compact star in conformal gravity have been studied. With the aim to find observational co…
We study the absorption of monochromatic electromagnetic plane waves impinging upon a Kerr black hole, in the general case that the direction of incidence is not aligned with the black hole spin axis. We present numerical results that are in accord with low- and high-frequency approximations. We find that circularly-polarized waves are distinguished by the black hole spin, with counter-rotating polarizations being more absorbed than co-rotating polarizations. At low frequencies and moderate incidence angles, there exists a narrow parameter window in which superradiant emission in the dipole mo…
The effect of electromagnetic radiation birefringence in the field of a relativistically rotating pulsar or magnetar within the framework of vacuum nonlinear electrodynamic
We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness…
We discuss the electromagnetic measurements of rotating observers and study the propagation of electromagnetic waves in a uniformly rotating frame of reference. The phenomenon of helicity-rotation coupling is elucidated and some of the observational consequences of the coupling of the spin of a particle with the rotation of a gravitational source are briefly examined.
It is well known fact that gravitational field can alter the space-time structure and gravitational redshift is its one example. Electromagnetic field can also alter the space-time similar to gravitational field. So electromagnetic field can give rise to an additional effect on gravitational redshift. There are many objects in nature, like neutron stars, magnetars etc which have high amount of rotation and magnetic field. In the present paper we will derive the expression of gravitational redshift from rotating body having intense magnetic field by using the action function of the electromagne…
We construct a new class of charged rotating black string solutions coupled to a nonlinear electromagnetic field in the background of anti-de Sitter spaces. We consider two types of nonlinear electromagnetic field namely, logarithmic and exponential forms. We investigate the geometric effects of nonlinearity parameter and find that for large $r$, these solutions recover the rotating back string solutions of Einstein-Maxwell theory. We calculate the conserved and thermodynamic quantities of the rotating black string. We also analyze thermodynamics of the spacetime and verify the validity of the…
A systematic rotation of the plane of polarization of electromagnetic radiation propagating over cosmological distances has been claimed to be detected by Nodland and Ralston.Taking the finite rotating universe of Oszvath and Schücking as a toy model for the actual universe,we calculate the rotation of the plane of polarization of electromagnetic waves in this universe.It turns out that the observed data are consistent with the Oszvath-Schücking parameter $k=0.39$.
We study analytically, via the Newman-Penrose formalism, the late time decay of scalar, electromagnetic, and gravitational perturbations outside a realistic rotating (Kerr) black hole. We find a power-law decay at timelike infinity, as well as at null infinity and along the event horizon (EH). For generic initial data we derive the power-law indices for all radiating modes of the various fields. We also give an exact analytic expression (accurate to leading order in 1/t) for the r-dependence of the late time tail at any r. Some of our main conclusions are: (i) For generic initial data, the lat…
The propagation of plane electromagnetic waves in the gravitational field inside a rotating cloud of dark matter is analyzed. Formulas for the deflection and absorption of light, and the rotation of the polarization plane are obtained in closed form in terms of the mass density and the angular velocity of the cloud. It is shown that the formulas can be considerably simplified for axisymmetric configurations. As an example, the formalism is applied to a rotating massive cloud described by a Plummer potential.
Perturbation techniques can be used as an alternative to supercomputer calculations in calculating gravitational radiation emitted by colliding black holes, provided the process starts with the black holes close to each other. We give a summary of the method and of the results obtained for various initial configurations, both axisymmetric and without symmetry: Initially static, boosted towards each other, counter-rotating, or boosted at an angle (pseudo-inspiral). Where applicable, we compare the perturbation results with supercomputer calculations.
We show that electromagnetic excitations of rotating black holes can lead to the appearance of narrow singular beams which break up the black hole horizon forming a tube-like region which connects the interior and exterior. It is argued that this effect may be at the origin of jet formation.
Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.
We study the structure of electromagnetic field of slowly rotating magnetized star in a Randall-Sundrum II type braneworld. The star is modeled as a sphere consisting of perfect highly magnetized fluid with infinite conductivity and frozen-in dipolar magnetic field. Maxwell's equations for the external magnetic field of the star in the braneworld are analytically solved in approximation of small distance from the surface of the star. We have also found numerical solution for the electric field outside the rotating magnetized neutron star in the braneworld in dependence on brane tension. The in…
A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state $3p + ε= constant$. We use a structural function for the Born-Infeld non-linear electrodynamics which is invariant under duality rotations and a metric possessing a four- parameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the Debever-Penrose vectors.
We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius $a$ at the equatorial plane.
The gravitational radiation emitted by a rotating magnetic dipole is calculated. Formulas for the polarization amplitudes and the radiated power are obtained in closed forms. A comparison is made with other sources of gravitational and electromagnetic radiation, particularly neutron stars with extremely powerful magnetic fields.
We consider a Kaluza-Klein vacuum solution which is closely related to the Gross-Perry-Sorkin (GPS) magnetic monopole. The solution can be obtained from the Euclidean Taub-NUT solution with an extra compact fifth spatial dimension within the formalism of Kaluza-Klein reduction. We study its physical properties as appearing in $(3+1)$ spacetime dimensions, which turns out to be a static magnetic monopole. We then boost the GPS magnetic monopole along the extra dimension, and perform the Kaluza-Klein reduction. The resulting four-dimensional spacetime is a rotating stationary system, with both e…
We study Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star and find analytical solutions for the exterior electric fields after separating the equations of electric field into angular and radial parts in the lowest order approximation. The star is considered isolated and in vacuum, with dipolar magnetic field aligned with the axis of rotation. The contribution to the external electric field of star from the NUT charge is considered in detail.
Rotating wormholes in Einstein-Dirac-Maxwell theory
Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic（吉尔吉斯共和国国家科学院J. Jeenbaev物理学家物理研究所）
In this paper we obtain an effective metric describing a regular and rotating magnetic black hole (BH) solution with a Yang-Mills electromagnetic source in Einstein-Yang-Mills (EYM) theory using the Newman--Janis algorithm via the non-complexification radial coordinate procedure. We then study the BH shadow and the quasinormal modes (QNMs) for massless scalar and electromagnetic fields and the quasiperiodic oscillations (QPOs). To this end, we also study the embedding diagram for the rotating EYM BH. The energy conditions, shadow curvature radius, topology and the dynamical evolution of scalar…
The accretion disk is formed by particles moving in closed orbits around a compact object, whose physical properties and the electromagnetic radiation characteristics are determined by the space-time geometry around the compact object. In this paper, we study the physical properties and the optical appearance of the electromagnetic radiation emitted from a thin accretion disk around the two types of the black hole solution in Einstein-Æther theory. We investigate in detail the effects of the æther field on the energy flux, temperature distribution, and electromagnetic spectrum of the disk in t…
We show the results of two dimensional general relativistic inviscid and isothermal hydrodynamical simulations comparing the behavior of co-rotating (with respect to the black hole rotation) and counter-rotating circumbinary quasi-Keplerian discs in the post merger phase of a supermassive binary black hole system. While confirming the spiral shock generation within the disc due to the combined effects of mass loss and recoil velocity of the black hole, we find that the maximum luminosity of counter-rotating discs is a factor ~(2-12) higher than in the co-rotating case, depending on the spin of…
Following the general formalism presented by Rezzolla, Ahmedov and Miller (MNRAS, 322, 723 2001), we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gr…
Motivated by the fact that the universe is dominated by dark matter and dark energy, we consider rotating black holes surrounded by perfect fluid dark matter and study the accretion process in thin disk around such black holes. Here, we are interested in how the presence of dark matter affects the properties of the electromagnetic radiation emitted from a thin accretion disk. For this purpose, we use the Novikov-Thorne model and obtain the electromagnetic spectrum of an accretion disk around a rotating black hole in perfect fluid dark matter and compare with the general relativistic case. The …
Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the "magic field" of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr-Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. …
We report on the occurrence of negative-phase-velocity (NPV) planewave propagation in the ergosphere of a rotating black hole. By implementing the Kerr metric, it is demonstrated that regions of NPV propagation are concentrated at the equator of the ergosphere, while NPV propagation is less common towards the polar regions. Increasing the angular velocity of the black hole exaggerates the NPV concentration at the equator. NPV propagation is not observed outside the stationary limit surface.
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…
Numerical simulations indicate that black holes carrying linear momentum and/or orbital momentum can power jets. The jets extract the kinetic energy stored in the black hole's motion. This could provide an important electromagnetic counterpart to gravitational wave searches. We develop the theory underlying these jets. In particular, we derive the analogues of the Penrose process and the Blandford-Znajek jet power prediction for boosted black holes. The jet power we find is $(v/2M)^2 Φ^2/(4π)$, where $v$ is the hole's velocity, $M$ is its mass, and $Φ$ is the magnetic flux. We show that energy…
Contrary to a prevailing assumption that black holes would swiftly discharge, we argue that black holes can charge preferentially when boosted through an ambient magnetic field. Though the details are very different, the preference for charge is related to the precipitation of the Wald charge on a spinning black hole in an ambient magnetic field. The gravito-electrodynamics upstage naive arguments about screening electric fields in determining the value of the charge accrued. Charged test particles, which build up the black hole charge, exhibit chaotic behavior as evidenced by fractal basin bo…
We examine energy conversion from accreting pair plasma to outgoing Poynting flux by black hole rotation. Our approach is based on a two-fluid model consisting of collisionless pair plasma. The electric potential is not constant along magnetic field lines, unlike an ideal magnetohydrodynamics approximation. We show how and where longitudinal electric fields and toroidal magnetic fields are generated by the rotation, whereas they vanish everywhere for radial flow in a split monopole magnetic field in a Schwarzschild black hole. Outgoing electromagnetic power in a steady state is calculated by a…
Pulsars are thought to be highly magnetized rotating neutron stars accelerating charged particles along magnetic field lines in their magnetosphere and visible as pulsed emission from the radio wavelength up to high energy X-rays and gamma-rays. Being highly compact objects with compactness close to $Ξ= R_s/R\approx0.5$, where $\Rs=2\,G\,M/c^2$ is the Schwarzschild radius and $\{M,R\}$ the mass and radius of the neutron star, general-relativistic effects become important close to their surface. This is especially true for the polar caps where radio emission is supposed to emanate from, leading…
We study high energy charged particle collisions near the horizon in an electromagnetic field around a rotating black hole and reveal the condition of the fine-tuning to obtain arbitrarily large center-of-mass (CM) energy. We demonstrate that the CM energy can be arbitrarily large as the uniformly magnetized rotating black hole arbitrarily approaches maximal rotation under the situation that a charged particle plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. Recently, Frolov [Phys. Rev. D 85, 024020 (2012)] proposed that the CM energy…
We study the formation of superradiant bound states for massive scalar fields in five-dimensional rotating black string geometries with a non-vanishing Kaluza-Klein momentum along the compact direction. Even though all Kaluza-Klein modes may form bound states in this geometry, in realistic extra-dimensional models and astrophysical black holes only the zero-mode is sufficiently light for superradiant instabilities to develop, provided the field has a small but non-vanishing mass, as for example for axion-like particles. We use analytical and numerical methods to show that, although the Kaluza-…
