We examine the behaviour of circular geodesics describing orbits of neutral test particles around an extreme Kerr-Newman black hole. It is well known that the radial Boyer-Lindquist coordinates of the prograde photon orbit $r=r_{\rm ph}$, marginally bound orbit $r=r_{\rm mb}$ and innermost stable orbit $r=r_{\rm ms}$ of the extreme Kerr black hole all coincide with the event horizon's value $r=r_+$. We find that for the extreme Kerr-Newman black hole with mass $M$, angular momentum $J$ and electric charge $Q=\pm\sqrt{M^2-J^2/M^2}$ ($|J|\le M^2$) the coordinate equalities $r_{\rm ph}=r_+$, $r_{\rm mb}=r_+$ and $r_{\rm ms}=r_+$ hold if and only if $|J|$ is greater than or equal to $M^2/2$, $M^2/\sqrt{3}$ and $M^2/\sqrt{2}$, respectively.
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.
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…
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.
In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We investigate the conditions for existence of bound orbits in causality-preserving region as well as the conditions for existence of circular orbits for charged and uncharged particles. We also study the effect of NUT parameter on Newtonian orbits. Finally, we give exact analytical solutions of equations of equatorial motion for a charged test particle.
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 $T_{\text{BH}}$.
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.
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…
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…
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.
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.
The recently proved `no short hair' theorem asserts that, if a spherically-symmetric static black hole has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the "photonsphere") of the corresponding black-hole spacetime: $r_{\text{field}}>r_{\text{null}}$. In this paper we provide compelling evidence that the bound can be {\it violated} by {\it non}-spherically symmetric hairy black-hole configurations. To that end, we analytically explore the physical properties of cloudy Kerr-Newman black-hole spacetimes -- charged rotating black holes which support lin…
We model the continuous material component of the Kerr-Newman disk as a discrete distribution of superluminal particles undergoing quantized orbital rotation with velocity $v/c = a/r$. By matching the discrete distribution in the continuous limit with the Kerr disk densities, we derive the quantized energy and momentum states of the superluminal orbits. We conclude that the Kerr-Newman disk may be modeled as a Dirac sea of these superluminal states and we identify possible excited states of the disk.
We find two conditions for superradiant instability of Kerr-Newman black holes under a charged massive scalar perturbation by analyzing asymptotic scalar potential and far-region wave function. Actually, they correspond to the condition for getting a trapping well. Also, we obtain the conditions for superradiant stability of Kerr-Newman black holes which states that there is no trapping well. The analysis is applied to Kerr black holes to find a condition for superradiant instability.
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.
In this paper, we revisit the possibilities of Bañados-Silk-West (BSW) effect in Kerr-Newman-Taub-NUT (KNTN) spacetime for two neutral particles moving over the equatorial plane and constant $θ$ in Boyer-Lindquist coordinate. Contrary to a previous study on this topic, we found that BSW effect for two particles confined to move over the equatorial plane is not possible. Numerical calculations shows that BSW effect in constant $θ$ geodesics is possible under certain circumstances.
We compute the second Seely-DeWitt coefficient of the kinetic operator of the metric and gauge fields in Einstein-Maxwell theory in an arbitrary background field configuration. We then use this result to compute the logarithmic correction to the entropy of an extremal Kerr-Newmann black hole.
The Cardy-Verlinde formula is further verified by using the Kerr-Newman-AdS$_4$ and Kerr-Newman-dS$_4$ black holes. In the Kerr-Newman-AdS$_4$ spacetime, we find that, for strongly coupled CFTs with AdS duals, to cast the entropy of the CFT into the Cardy-Verlinde formula the Casimir energy must contains the terms $ -n ({\mathcal{J}} Ω_H+ \frac{QΦ}{2}+ \frac{QΦ_0}{2})$, which associate with rotational and electric potential energies, and the extensive energy includes the term $-Q Φ_0$. For the Kerr-Newman-dS$_4$ black hole, we note that the Casimir energy is negative but the extensive energy i…
The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schrödinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of obtaining effective potentials is generalized. Effective potentials have isolated singularities on the event horizons as well as at certain parameters of the Kerr-Newman field and of the fermion in the neighborhoods of some values of the radial coordinate. For the extreme Kerr-Newman field, the impossibility of existence of stationary bound states of half-spin part…
The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein--Maxwell gravity (the Kerr--Newman solution) and low-energy heterotic string theory (the Kerr--Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black ho…
The canonical approach to black hole entropy in Poincaré gauge theory without matter is extended to include Maxwell field as a matter source. The new formalism is used to calculate asymptotic charges and entropy of Kerr--Newmann--AdS black holes with torsion. The result implies that the first law, with a nontrivial contribution of the Maxwell field, takes the same form as in general relativity.
We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.
By employing a pseudo-orthonormal coordinate-free approach, the Dirac equation for particles in the Kerr--Newman spacetime is separated into its radial and angular parts. In the massless case to which a special attention is given, the general Heun-type equations turn into their confluent form. We show how one recovers some results previously obtained in literature, by other means.
In this paper we argue that the well-known maximal extensions of the Kerr and Kerr-Newman spacetimes characterized by a specific gluing (on disks) of two asymptotically flat regions with ADM masses of opposite signs are physically inconsistent and actually non-analytic. We also discover a correct geometrical interpretation of the surface $r=0$, $t={\rm const}$ - a dicone in the case of the Kerr solution and a more sophisticated surface of non-zero Gaussian curvature in the case of the Kerr-Newman solution - which suggests that the problem of constructing the maximal analytic extensions for the…
We find that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value and the shadowless-ness may be related to the appearance of the null hypersurface caustics (NHC) both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
By applying a set of Hassan-Sen transformations and string dualities to the Kerr-Godel solution of minimal D=5 supergravity we derive a four parameter family of five dimensional solutions in type II string theory. They describe rotating, charged black holes in a rotating background. For zero background rotation, the solution is D=5 Kerr-Newman; for zero charge it is Kerr-Godel. In a particular extremal limit the solution describes an asymptotically Godel BMPV black hole.
We study the Hawking thermal spectrum in dragging coordinate system and the tunneling radiation characteristics of hot NUT-Kerr-Newman-Kasuya spacetime. The tunneling rates at the event and cosmological horizon are found to be related to the change of Bekenstein-Hawking entropy. The radiation spectrum is not pure thermal and thus there is a correction to the Hawking thermal spectrum.
An attempt is made to supplement Carter's partial investigation of the global structure of Kerr-Newman spacetime on the symmetry axis. Namely, the global structure of θ= const. timelike submanifolds of Kerr-Newman metric starting from the symmetry axis all the way down to the equatorial plane are studied by introducing a new time coordinate slightly different from the usual Boyer-Lindquist time coordinate. It turns out that the maximal anaytic extension of θ= θ_0 (0 \leq θ_0 < π/2) submanifolds is the same as that of the symmetry axis first studied by Carter whereas θ= π/2 equatorial plane has…
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
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 find generators of the conformal symmetry for the class of Kerr-Newman-NUT-AdS black holes from the deformed scalar probe equation. We find two classes of solutions for the generators (also known as conformal J and Q pictures). The two classes of deformed generators are the extension of similar generators for the regular conformal symmetry. Moreover, we find that the two pictures can be generalized and extended into a general picture. In each picture, the generators produce an extended local family of SL(2,R)_L \times SL(2,R)_R hidden conformal symmetries for the Kerr-Newman-NUT-AdS black h…
We study $\mathcal{N}=2$ supergravity with higher-derivative corrections that preserve the $\mathcal{N}=2$ supersymmetry and show that Kerr-Newman black holes are solutions to these theories. Modifications of the black hole entropy due to the higher derivatives are universal and apply even in the BPS and Schwarzschild limits. Our solutions and their entropy are greatly simplified by supersymmetry of the theory even though the black holes generally do not preserve any of the supersymmetry.
We find an exact solution of Kerr-Newman-de Sitter type on the braneworld(4D) of the DGP model. When a constant 4D Ricci scalar is assumed, only zero(flat) and a positive(de-Sitter) values satisfy the Hamiltonian constraint equation coming from the extra dimension. With a Z_2-symmetry across the brane and a stationary and axisymmetric metric ansatz on the brane, we solve the constraint equation exactly in the Kerr-Schild form with de-Sitter background. In the de-Sitter background this Kerr-Schild solution is well behaved under Boyer-Lindquist transformation: the constraint equation is preserve…
Discussion of the equatorial photon motion in Kerr-Newman black-hole and naked-singularity spacetimes with a non-zero cosmological constant is presented. Both repulsive and attractive cosmological constants are considered. Circular photon orbits are determined, and their stability is established. The spacetimes are divided into separated classes according to the properties of the `effective potential'. There is a special class of Kerr-Newman-de Sitter black-hole spacetimes with so-called `restricted repulsive barrier'. Further, the azimuthal motion is discussed and photon trajectories are give…
We discuss the relation of the Kerr-Newman spinning particle to the Dirac electron and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the Kerr-Newman geometry. As a result, the Dirac electron acquires an extended space-time structure of the Kerr-Newman geometry - singular ring of the Compton size and twistorial polarization of the gravitational and electromagnetic fields. Behavior of this Dirac -- Kerr-Newman system in the weak and slowly changed electromagnetic fields is determined by the wave function of the Dirac equati…
Charged, rotating Kerr-Newman black holes represent the most general class of asymptotically flat black hole solutions to the Einstein-Maxwell equations of general relativity. Here, we consider a simplified model for the Hawking radiation produced by a Kerr-Newman black hole by utilising a (1+1)-dimensional accelerated boundary correspondence (i.e. a flat spacetime mirror trajectory) in Minkowski spacetime. We derive the particle spectrum and its late-time thermal distribution which reduces to the Kerr, Reissner-Nordström and Schwarzschild cases in the appropriate limits. We also compute the p…
We present a detailed analysis of the orbital circular motion of electrically neutral test particles on the equatorial plane of the Kerr-Newman spacetime. Many details of the motion in the cases of black hole and naked singularity sources are pointed out. We identify four different types of orbital regions, which depend on the properties of the orbital angular momentum, and define four different kinds of naked singularities, according to the values of the charge-to-mass ratio of the source. It is shown that the presence of a particular type of counter-rotating test particles is sufficient to u…
The Kerr-Newman metric describes a very special rotating, charged mass and is the most general of the asymptotically flat stationary 'black hole' solutions to the Einstein-Maxwell equations of general relativity. We review the derivation of this metric from the Reissner-Nordstrom solution by means of a complex transformation algorithm and provide a brief overview of its basic geometric properties. We also include some discussion of interpretive issues, related metrics, and higher-dimensional analogues.
The charged, spinning and gravitating soliton is realized as a regular solution of the Kerr-Newman field coupled with a chiral Higgs model. A regular core of the solution is formed by a domain wall bubble interpolating between the external Kerr-Newman solution and a flat superconducting interior. An internal electromagnetic (em) field is expelled to the boundary of the bubble by the Higgs field. The solution reveals two new peculiarities: (i) the Higgs field is oscillating, similar to the known oscillon models, (ii) the em field forms on the edge of the bubble a Wilson loop, resulting in quant…
We show the generic non-extremal Kerr-Newman-NUT-AdS black holes are holographically dual to the hidden conformal field theories in two different pictures. The two pictures can be merged together to the dual CFTs in general picture, that are generated by the $SL(2,\mathbb{Z})$ modular group. We also extend the calculation to the extremal limit and find the corresponding quantities. Using the extended central charges from the Kerr/CFT correspondence, we also find agreement between the macroscopic and microscopic entropies. We also find the absorption cross-section of the scalar probes for the g…
The Brown-York quasi-local energy of a charged rotating black hole described by the Kerr-Newman metric and enclosed by a fixed-radius surface is computed. No further assumptions on the angular momentum or the radial coordinate in Boyer-Lindquist coordinates were made. The result can be expressed in terms of incomplete elliptic integrals and is used to analyze the self-energy of an electron which is assumed to be described by the Kerr-Newman metric. For this purpose the small sphere limit is investigated thoroughly comparing the analysis with known results. Evaluating the energy using the mass,…
In this paper, we employ the general equatorially symmetric two-soliton solution of the Einstein-Maxwell equations for elaborating two physically meaningful configurations describing a pair of equal Kerr-Newman corotating black holes separated by a massless strut. The first configuration is characterized by opposite magnetic charges of its constituents, while in the second configuration the black holes carry equal electric and opposite magnetic charges, thus providing a nontrivial example of a binary dyonic black-hole system. The thermodynamic properties of these binary configurations are stud…
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.
Generalized Painleve-Gullstrand metrics are explicitly constructed for the Kerr-Newman family of charged rotating black holes. These descriptions are free of all coordinate singularities; moreover, unlike the Doran and other proposed metrics, an extra tunable function is introduced to ensure all variables in the metrics remain real for all values of the mass M, charge Q, angular momentum aM, and cosmological constant Λ> - 3/(a^2). To describe fermions in Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein one-forms at the horizon(s) is imposed and coordinate singularities…
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.
We present a simple approach for obtaining Kerr interior solutions with the help of the Newman-Janis algorithm (NJA) starting with static space-times describing physically sensible interior Schwarzschild solutions. In this context, the Darmois-Israel (DI) junction conditions are analyzed. Starting from the incompressible Schwarzschild solution, a class of Kerr interior solutions is presented, together with a discussion of the slowly rotating limit. The energy conditions are discussed for the solutions so obtained. Finally, the NJA algorithm is applied to the static, anisotropic, conformally fl…
In this paper, we consider the rotating charged Gödel black hole and study the effect of the higher order corrections of the entropy on the thermodynamics and statistics quantities of the Kerr-Newman-Gödel black hole. The leading order correction is logarithmic while higher-order terms are proportional to the inverse of the area of the black hole. We obtain modified thermodynamics and statistics and find that correction terms are important in the stability of the black hole.
A simple yet systematic new algorithm to investigate the global structure of Kerr-Newman spacetime is suggested. Namely, the global structure of θ=const. timelike submanifolds of Kerr-Newman metric are studied by introducing a new time coordinate slightly different from the usual Boyer-Lindquist time coordinate. In addition, it is demonstrated that the possible causality violation thus far regarded to occur near the ring singularity via the development of closed timelike curves there is not really an unavoidable pathology which has plagued the Kerr-Newman solution but simply a gauge (coordinat…
We compute numerically the quasinormal modes of Kerr-Newman black holes in the scalar case, for which the perturbation equations are separable. Then we study different approximations to decouple electromagnetic and gravitational perturbations of the Kerr-Newman metric, computing the corresponding quasinormal modes. Our results suggest that the Teukolsky-like equation derived by Dudley and Finley gives a good approximation to the dynamics of a rotating charged black hole for Q<M/2. Though insufficient to deal with Kerr-Newman based models of elementary particles, the Dudley-Finley equation shou…
In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained.
The Kerr-Newman solution with negative mass is shown to develop a massless ring singularity off the symmetry axis. The singularity is located inside the region with closed timelike curves which has topology of a torus and lies outside the ergoregion. These characteristics are also shared by the charged Tomimatsu-Sato delta=2 solution with negative total mass to which in particular a simple form in terms of four polynomials is provided.
