The gravitational deflection of test particles including light, due to a radially moving Kerr-Newman black hole with an arbitrary constant velocity being perpendicular to its angular momentum, is investigated. In harmonic coordinates, we derive the second post-Minkowskian equations of motion for test particles, and solve them by high-accuracy numerical calculations. We then concentrate on discussing the kinematical corrections caused by the motion of the gravitational source to the second-order deflection. The analytical formula of light deflection angle up to second order by the moving lens is obtained. For a massive particle moving with a relativistic velocity, there are two different analytical results for Schwarzschild deflection angle up to second order reported in the previous works, i.e., $α(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+3π\left(\frac{1}{4}+\frac{1}{w^2}\right)\frac{M^2}{b^2}$ and $α(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+\left[3π\left(\frac{1}{4}+\frac{1}{w^2}\right)+2\left(1-\frac{1}{w^4}\right)\right]\frac{M^2}{b^2}$, where $M,$ $b,$ and $w$ are the mass of the lens, impact parameter, and the particle's initial velocity, respectively. Our numerical result is in perfect agreement with the former. Furthermore, the analytical formula for massive particle deflection up to second order in the Kerr geometry is achieved. Finally, the possibilities of detecting the motion effects on the second-order deflection are also analyzed.
In this work, we base on the second-order post-Minkowskian equations of motion, and apply an iterative technique to analytically derive the gravitational deflection of the relativistic particles in the equatorial plane of Kerr-Newman black hole with a radial (or longitudinal) and constant velocity. We find that the kinematically correctional effects on the second-order contributions to the deflection can be expressed into a very compact form, which are valid for both the massive particle and photon. Our result reduces to the previous formulation for the first-order deflection caused by a movin…
In this work, we study the weak gravitational lensing in the background of Kerr-Newman black hole with quintessential dark energy. Initially, we compute the deflection angle of light by charged black hole with quintessential dark energy by utilizing the Gauss-Bnnet theorem. Firstly, we suppose the light rays on the equatorial plane in the axisymmetric spacetime. In doing so, we first find the corresponding optical metrics and then calculate the Gaussian optical curvature to utilize in Gauss-Bonnet theorem. Consequently, we calculate the deflection angle of light for rotating charged black hole…
Source-free equations of nonlinear electrodynamics minimally coupled to gravity (NED-GR) admit regular axially symmetric asymptotically Kerr-Newman solutions, which describe electrically charged rotating black holes and spinning solitons. Asymptotic analysis of solutions shows the existence of de Sitter vacuum interior which has the properties of a perfect conductor and an ideal diamagnetic. The Kerr ring singularity (a naked singularity in the case without horizons) is replaced with a superconducting current, which serves as a nondissipative source of the Kerr-Newman fields and can be respons…
We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constituted by the particles' initial velocity unit vector, impact vector, and their cross-product. The achieved formulas explicitly give the dependences of the particles' trajectory and velocity on the time once their initial position and velocity are specified, and can be applied not only to a massive particle, but also to a photon as well.
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.
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…
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.
We present the first systematic study of the gravitational collapse of rotating and magnetised neutron stars to charged and rotating (Kerr-Newman) black holes. In particular, we consider the collapse of magnetised and rotating neutron stars assuming that no pair-creation takes place and that the charge density in the magnetosphere is so low that the stellar exterior can be described as an electrovacuum. Under these assumptions, which are rather reasonable for a pulsar that has crossed the 'death line', we show that when the star is rotating, it acquires a net initial electrical charge, which i…
We study the shadow cast or silhouette generated by a Kerr-Newman-Kasuya (KNK) spacetime (rotating dyon black hole). It is shown that in addition to the angular momentum of the black hole, the dyon charge also affects the shadow image of the KNK black hole. Moreover, we analyze the weak gravitational lensing by the KNK black hole by using the Gauss-Bonnet theorem. Finally, we find that extra dyon charge decreases both the deflection angle and shadow of the KNK black hole.
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…
By using an analytic solution of the Teukolsky equation in the Kerr-de Sitter and Kerr-Newman-de Sitter geometries, an analytic expression of the absorption rate formulae for these black holes is calculated.
We present new rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory of gravity. For this task, we consider scalar-flat Weyl-Cartan geometries and obtain an axisymmetric Kerr-Newman solution in the decoupling limit between the orbital and the spin angular momentum. The corresponding Kerr-Newman-de Sitter solution is also compatible with a cosmological constant and additional electromagnetic fields.
We check the weak cosmic censorship conjecture by attempting to overspin the Kerr-Newman-Kasuya black hole with test particle. The study suggests that the Kerr-Newman-Kasuya black hole can be over-spun showing the violation of cosmic censorship conjecture.
The analytic solution of Teukolsky equation in Kerr-de Sitter and Kerr-Newman-de Sitter geometries is presented and the properties of the solution are examined. In particular, we show that our solution satisfies the Teukolsky-Starobinsky identities explicitly and fix the relative normalization between solutions with the spin weight $s$ and $-s$.
In this paper, we review the one-dimensional quantum channel and investigate Hawking radiation of bosons and fermions in Kerr and Kerr-Newman black holes. The result shows the Hawking radiation can be described by the quantum channel. The thermal conductances are derived and related to the black holes' temperatures.
Using the Pöshl-Teller approximation, we evaluate the neutrino quasinormal modes (QNMs) of a Kerr-Newman-de Sitter black hole. The result shows that for a Kerr-Newman-de Sitter black hole, massless neutrino perturbation of large $Λ$, positive $m$ and small value of $n$ will decay slowly.
The coupled gravitational-electromagnetic quasinormal resonances of charged rotating Kerr-Newman black holes are explored. In particular, using the recently published numerical data of Dias, Godazgar, and Santos [Phys. Rev. Lett. 114, 151101 (2015)], we show that the characteristic relaxation times $τ\equiv 1/\Imω_0$ of near-extremal Kerr-Newman black holes in the regime $Q/r_+\leq 0.9$ are described, to a very good degree of accuracy, by the simple universal relation $τ\times T_{\text{BH}}=π^{-1}$ (here $Q, r_+$, and $T_{\text{BH}}$ are respectively the electric charge, horizon radius, and te…
We show that the domains of dependence of stationary, $I^+$-regular, analytic, electrovacuum space-times with a connected, non-empty, rotating, degenerate event horizon arise from Kerr-Newman space-times.
According to the no-hair theorem, the Kerr-Newman black hole solution represents the most general asymptotically flat, stationary (electro-) vacuum black hole solution in general relativity. The procedure described here shows how this solution can indeed be constructed as the unique solution to the corresponding boundary value problem of the axially symmetric Einstein-Maxwell equations in a straightforward manner.
The resonant mode spectrum of the Kerr-Newman spacetime is presently unknown. These modes, called the quasinormal modes, play a central role in determining the stability of Kerr-Newman black holes and their response to perturbations. We present a new formalism, generalized from time-independent perturbation theory in quantum mechanics, for calculating the quasinormal mode frequencies of weakly charged Kerr-Newman spacetimes of arbitrary spin. Our method makes use of an original technique for applying perturbation theory to zeroth-order solutions that are not square- integrable, and it can be a…
In a recent paper (arXiv:1410.0694) Zilhão, Cardoso, Herdeiro, Lehner, and Sperhake have studied the nonlinear stability of Kerr-Newman black holes. We show that their numerical results for the time evolutions of the spacetime deformations of near-extremal Kerr-Newman black holes are described extremely well by a {\it universal} formula for the quasinormal resonances of the black holes. This formula is expressed in terms of the black-hole physical parameters: the horizon angular velocity $Ω_{\text{H}}$ and the Bekenstein-Hawking temperature $T_{\text{BH}}$.
Membrane method is used to compute the entropy of the NUT-Kerr-Newman black holes. It is found that even though the Euler characteristic is greater than two, the Bekenstein-Hawking area law is still satisfied. The formula $S=χA/8$ relating the entropy and the Euler characteristic becomes inapplicable for non-extreme four dimensional NUT-Kerr-Newman black holes.
A new proof of the uniqueness of the Kerr-Newman black hole solutions amongst asymptotically flat, stationary and axisymmetric electro-vacuum spacetimes surrounding a connected Killing horizon is given by means of an explicit construction of the corresponding complex Ernst potentials on the axis of symmetry. This construction, which makes use of the inverse scattering method, also works in the case of a degenerate horizon.
The Kerr-Newman black hole solution can be constructed straightforwardly as the unique solution to the boundary value problem of the Einstein-Maxwell equations corresponding to an asymptotically flat, stationary and axisymmetric electro-vacuum spacetime surrounding a connected Killing horizon.
Using the Kerr-Schild decomposition of the metric tensor that employs the algebraically special nature of the Kerr-Newman space-time family, we calculate the energy-momentum tensor. The latter turns out to be a well-defined tensor-distribution with disk-like support.
It is shown that, in the case of Kerr-Newman space-time, the complex electromagnetic strength E + i H and analogous complex intensity of the gravitational field share the common complexified spatial direction.
A three-dimensional light-like foliation of a spacetime geometry is one particular way of studying its light cone structure and has important applications in numerical relativity. In this paper, we execute such a foliation for the Kerr-Newman-AdS black hole geometry and compare it with the lightlike foliations of the Kerr-AdS and Kerr-Newman black holes. We derive the equations that govern this slicing and study their properties. In particular, we find that these null hypersurfaces develop caustics inside the inner horizon of the Kerr-Newman-AdS black hole, in strong contrast to the Kerr-AdS c…
Gaussian curvature of the two-surface r=0, t=const is calculated for the Kerr-de Sitter and Kerr-Newman-de Sitter solutions, yielding non-zero analytical expressions for both the cases. The results obtained, on the one hand, exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions.
The Kerr metric is known to present issues when trying to find an interior solution. In this work we continue in our efforts to construct a more realistic exterior metric for astrophysical objects. A new approximate metric representing the spacetime of a charged, rotating and slightly-deformed body is obtained by perturbing the Kerr-Newman metric to include the mass-quadrupole and quadrupole-quadrupole orders. It has a simple form, because is Kerr-Newman-like. Its post-linear form without charge coincides with post-linear quadrupole-quadrupole metrics already found.
A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordstrom and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric.
The second-order post-Newtonian solution for the light propagation in the field of Kerr-Newman black hole is achieved via an iterative method. Based on this result, we further obtain the second-order post-Newtonian light deflection in Kerr-Newman spacetime, which is formulated in an united form for any arbitrarily incident directions. All results are exhibited in the coordinate system constituted by the initial light-direction vector, the impact vector, and their cross-product.
We show that non-degenerate multiple black hole solution of Einstein- Maxwell equations in an asymptotically flat axisymmetric spacetime cannot be in stationary equilibrium. This extends the uniqueness of Kerr-Newman solution first proved by Bunting and Mazur in a much wider desirable class. Spin-spin interaction cannot hold the black hole aparts even with electromagnetic forces.
The energy distribution in the Kerr-Newman space-time is computed using the Møller energy-momentum complex. This agrees with the Komar mass for this space-time obtained by Cohen and de Felice. These results support the Cooperstock hypothesis.
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
Charged rotating Kerr-Newman black holes are known to be superradiantly unstable to perturbations of charged massive bosonic fields whose proper frequencies lie in the bounded regime $0 < ω< \text{min} \{ω_{\text{c}} \equiv m Ω_{\text{H}} + qΦ_{\text{H}},μ\}$ [here $\{Ω_{\text{H}}, Φ_{\text{H}}\}$ are respectively the angular velocity and electric potential of the Kerr-Newman black hole, and $\{m,q,μ\}$ are respectively the azimuthal harmonic index, the charge coupling constant, and the proper mass of the field]. In this paper we study analytically the complex resonance spectrum which characte…
Applying a dimensional reduction technique and a coordinates transformation approach, we deduce the Kerr-Newman space-time into a Painlevé-like form, and obtain its corresponding event horizon and the Hawking radiation temperature. We find that, the event horizon of a Kerr-Newman black hole can be simulated in a superconducting transmission line. Moreover, by running some numerical simulation, we confirm that the Hawking radiation of a Kerr-Newman Black Hole can be experimentally measured in a superconducting transmission line.
We prove a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-time must be one of the Kerr-Newman solutions. The closeness to the Kerr-Newman family is measured by the smallness of a pair of Mars-Simon type tensors, which were introduced by Wong in \cite{Wong_09} to detect the Kerr-Newmann family.
The explicit form for the post-Newtonian gravitational time delay of light signals propagating on the equatorial plane of a Kerr-Newman black hole is derived. Based on the null geodesic in Kerr-Newman spacetime, we adopt the iterative method to calculate the time delay. Our result reduces to the previous formulation for Kerr black hole if we drop off the contribution from the electrical charge. Our time-delay formula for the Reissner-Nordström geometry is different from the previous publication [Phys. Rev. D 69, 023002 (2004)], in which the largest second-order contribution to the time delay i…
In this article, the superradiation stability of Kerr-Newman black holes is discussed by introducing the condition used in Kerr black holes y into them. Moreover, the motion equation of the minimal coupled scalar perturbation in a Kerr-Newman black hole is divided into angular and radial parts. Hod proved\cite{12} that the Kerr black hole should be superradiantly stable under massive scalar perturbation when $μ\ge \sqrt{2}mΩ_H$, where $μ$ is the mass. In this article, a new variable y is added here to expand the results of the above article. When $\sqrt{2(a^2+Q^2)}/{r^2_+}< ω< m\varOmega_H+q\v…
In the present paper, the characterization of the Kerr metric found by Marc Mars is extended to the Kerr-Newman family. A simultaneous alignment of the Maxwell field, the Ernst two-form of the pseudo-stationary Killing vector field, and the Weyl curvature of the metric is shown to imply that the space-time is locally isometric to domains in the Kerr-Newman metric. The paper also presents an extension of Ionescu and Klainerman's null tetrad formalism to explicitly include Ricci curvature terms.
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 …
We prove the possibility of existence of stationary bound states of stationary bound states of spin-half probe particles for the Kerr and Kerr-Newman gravitational fields using Chandrasekhar's Hamiltonian. If the Hilbert condition is satisfied, g_{00}>0, bound states of Dirac particles with a real discrete energy spectrum can exist both for particles outside the surface of the outer ergosphere of the Kerr and Kerr-Newman fields, and for particles under the surface of the inner ergosphere. In this case, the surfaces of the external and internal ergospheres play the role of infinitely high poten…
If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal Kerr-Newman-AdS black hole could lead to destroy their event horizon, giving rise to naked singularities. Hence radiative and self-force effects must be taken into account to further test cosmic censorship. Moreover, the allowed parameter range for this test particle is very narrow, this leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-AdS spacetime.
We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so characterises this type of data. We first illustrate the characterisation of the Kerr-Newman spacetime in terms of Killing spinors. The space spinor formalism is then used to obtain a set of four independent conditions on an initial Cauchy hypersurface that guarantee the existence of a Killing spinor on the development of the initial data. Following a similar a…
We study the family of Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant. This leads to a quantisation condition on the masses and charges of the resulting Euclidean solutions.
Generalising arXiv:1511.08496, we construct further families of compact Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant.
An electromagnetic analog of the Kerr-Newman solution in general relativity is derived, based on Minkowski's formulation for electromagnetic fields in moving media. The equivalent system is a distribution of charges and currents largely localized within a spinning disk of radius a. This occurs in a rotating medium of inhomogeneous index of refraction and "frame dragging" at exactly half the angular velocity of the electrical charge.
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…
We show that the Hawking temperature is modified in the presence of dark energy in an emergent gravity scenario for Kerr-Newman(KN) and Kerr-Newman-AdS(KNAdS) background metrics. The emergent gravity metric is not conformally equivalent to the gravitational metric. We calculate the Hawking temperatures for these emergent gravity metrics along $θ=0$. Also we show that the emergent black hole metrics are satisfying Einstein's equations for large $r$ and $θ=0$. Our analysis is done in the context of dark energy in an emergent gravity scenario having $k-$essence scalar fields $ϕ$ with a Dirac-Born…
We prove that the only four dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a longstanding gap in the black hole uniqueness theorems.
We find a new class of exact solutions in the Einstein-Maxwell theory by employing the Ernst magnetization process to the Kerr-Newman-Taub-NUT spacetimes. We study the solutions and find that they are regular everywhere. We also find the quasilocal conserved quantities for the spacetimes, the corresponding Smarr formula and the first law of thermodynamics.
The Newman-Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not a…
It is very important to calculate the amount of radiation from a black hole as the radiation from a black hole contributes to its entropy. In this paper I have calculated the Entropy of a black hole from the action. I have used path integral formalism to calculate the second order perturbation of the metric in the action for a generalized Kerr-Newman metric.
