Kerr-Newman Research Articles

New form of the Kerr-Newman solution

A new form of the Kerr-Newman solution is presented. The solution involves a time coordinate which represents the local proper time for a charged massive particle released from rest at spatial infinity. The chosen coordinates ensure that the solution is well-behaved at horizons and enable an intuitive description of many physical phenomena. If the charge of the particle $e = 0$, the coordinates reduce to Doran coordinates for the Kerr solution with the replacement $M \to M - Q^2/(2r)$, where $M$ and $Q$ are the mass and charge of the black hole, respectively. Such coordinates are valid only for $r \ge Q^2/(2M)$, however, which corresponds to the region that a neutral particle released from rest at infinity can penetrate. By contrast, for $e \neq 0$ and of opposite sign to $Q$, the new coordinates have a progressively extended range of validity as $|e|$ increases and tend to advanced Eddington-Finkelstein (EF) null coordinates as $|e| \to \infty$, hence becoming global in this limit. The Kerr solution (i.e.\ with $Q=0$) may also be written in terms of the new coordinates by setting $eQ = -\alpha$, where $\alpha$ is a real parameter unrelated to charge; in this case the coordinate system is global for all non-negative values of $\alpha$ and the limits $\alpha = 0$ and $\alpha \to \infty$ correspond to Doran coordinates and advanced EF null coordinates, respectively, without any need to transform between them.

Topological classes of rotating black holes

In this paper, we investigate the topological numbers for the singly rotating Kerr black holes in all dimensions and the four-dimensional Kerr-Newman black hole. We show that for uncharged black holes, the rotation parameter has a significant effect on the topological number, and for rotating black holes, the dimension of spacetimes has a remarkable effect on the topological number too. In addition, we find that the topological numbers of the four-dimensional Kerr and Kerr-Newman black holes are the same, which seems to indicate that the electric charge parameter has no effect on the topological number of rotating black holes. Our current research provides more evidence that the conjecture put forward in Wei et al. [Phys. Rev. Lett., 129, 191101 (2022)], according to which all black hole solutions should be separated into three different topological classes, is accurate, at least in the pure Einstein-Maxwell gravity theory.

Analytic kludge waveforms for extreme-mass-ratio inspirals of a charged object around a Kerr-Newman black hole

We derive the approximate, ``analytic-kludge'' (AK) waveforms for the inspiral of a charged stellar-mass compact object (CO) into a charged massive Kerr-Newman (KN) black hole (BH). The modifications of the inspiral orbit due to the charges in this system can be attributed to three sources: the electric force between the CO and the MBH, the energy flow of the dipole electromagnetic radiation, and the deformation of the metric caused by the charge of the MBH. All these are encoded explicitly in the fundamental frequencies of the orbits, which are calculated analytically in the weak-field regime. By calculating the mismatch between the waveforms for charged and neutral EMRI systems with respect to space-borne detectors TianQin and LISA, we show that tiny charges in the system can produce distinct imprints on the waveforms. Finally, we perform parameter estimation for the charges using the Fisher information matrix method and find that the precision can reach the level of $10^{-5}$ in suitable scenarios. We also study the effects of charges on the parameter estimation of charge, where the effects from the charge of the MBH can be well explained by its effects on the cutoff of the inspiral.

Anyonic spin-Hall effect on the black hole horizon

Using the fact that the horizon of black holes is a Carroll manifold, we show that an ``exotic photon'' i.e. a particle without mass and charge but with anyonic spin, magnetic moment and ``exotic'' charges associated with the 2-parameter central extension of the 2-dimensional Carroll group moves on the horizon of a Kerr-Newman Black Hole consistently with the Hall law.

Explicit Symplectic Methods in Black Hole Spacetimes

Many Hamiltonian problems in the solar system are separable into two analytically solvable parts, and thus serve as a great chance to develop and apply explicit symplectic integrators based on operator splitting and composing. However, such constructions are not in general available for curved spacetimes in general relativity and modified theories of gravity because these curved spacetimes correspond to nonseparable Hamiltonians without the two-part splits. Recently, several black hole spacetimes such as the Schwarzschild black hole were found to allow for the construction of explicit symplectic integrators, since their corresponding Hamiltonians are separable into more than two explicitly integrable pieces. Although some other curved spacetimes including the Kerr black hole do not have such multipart splits, their corresponding appropriate time-transformation Hamiltonians do. In fact, the key problem in obtaining symplectic analytically integrable decomposition algorithms is how to split these Hamiltonians or time-transformation Hamiltonians. Considering this idea, we develop explicit symplectic schemes in curved spacetimes. We introduce a class of spacetimes whose Hamiltonians are directly split into several explicitly integrable terms. For example, the Hamiltonian of a rotating black ring has a 13-part split. We also present two sets of spacetimes whose appropriate time-transformation Hamiltonians have the desirable splits. For instance, an eight-part split exists in a time-transformed Hamiltonian of a Kerr–Newman solution with a disformal parameter. In this way, the proposed symplectic splitting methods can be used widely for long-term integrations of orbits in most curved spacetimes we know of.

Null and timelike geodesics in the Kerr-Newman black hole exterior

We study the null and time-like geodesics of the light and the neutral particles respectively in the exterior of Kerr-Newman black holes. The geodesic equations are known to be written as a set of first-order differential equations in Mino time from which the angular and radial potentials can be defined. We classify the roots for both potentials, and mainly focus on those of the radial potential with an emphasis on the effect from the charge of the black holes. We then obtain the solutions of the trajectories in terms of the elliptical integrals and the Jacobian elliptic functions for both null and time-like geodesics, which are manifestly real functions of the Mino time that the initial conditions can be explicitly specified. We also describe the details of how to reduce those solutions into the cases of the spherical orbits. The effect of the black hole's charge decreases the radii of the spherical motion of the light and the particle for both direct and retrograde motions. In particular, we focus on the light/particle boomerang of the spherical orbits due to the frame dragging from the back hole's spin with the effect from the charge of the black hole. To sustain the change of the azimuthal angle of the light rays, say for example $\Delta \phi=\pi$ during the whole trip, the presence of the black hole's charge decreases the radius of the orbit and consequently reduces the needed values of the black hole's spin. As for the particle boomerang, the particle's inertia renders smaller change of the angle $\Delta \phi$ as compared with the light boomerang. Moreover, the black hole's charge also results in the smaller angle change $\Delta \phi$ of the particle than that in the Kerr case. The implications of the obtained results to observations are discussed.

Love symmetry

Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2, ℝ) symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2, ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2, ℝ) representations. It is this highest weight properety that forces the static Love numbers to vanish. We find that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. This relation is simplest for extremal charged spherically symmetric (Reissner-Nordström) solutions, where the Love symmetry exactly reduces to the isometry of the near horizon AdS2 throat. For rotating (Kerr-Newman) black holes one is lead to consider an infinite-dimensional SL(2, ℝ) ⋉ hat{textrm{U}}{(1)}_{mathcal{V}} extension of the Love symmetry. It contains three physically distinct subalgebras: the Love algebra, the Starobinsky near zone algebra, and the near horizon algebra that becomes the Bardeen-Horowitz isometry in the extremal limit. We also discuss other aspects of the Love symmetry, such as the geometric meaning of its generators for spin weighted fields, connection to the no-hair theorems, non-renormalization of Love numbers, its relation to (non-extremal) Kerr/CFT correspondence and prospects of its existence in modified theories of gravity.

Gravitating Electron Based on Overrotating Kerr-Newman Solution

We consider a consistent with gravity electron based on the overrotating Kerr-Newman (KH) solution and show that the earlier KH electron models proposed by Carter, Israel and López in 1970–1990 should be modified by the Landau-Ginzburg theory, leading to a superconducting electron model consistent with gravity and quantum theory. Truncated by Israel and López, the second sheet of the KN solution is rearranged and represented in a mirror form as a sheet of the positron, so that the modified KN system forms a quantum electron-positron vacuum interacting with gravity. Regularization of the KN black hole solution creates two new important effects leading to a strong gravitational interaction that acts on the Compton scale contrary to the usual Planck scale of Schwarzschild gravity: (A)—gravitational frame-dragging creates two Wilson loops acting at two boundaries of the modified KN solution, and (B)—formation of the flat superconducting core of the regularized KN solution creates a superconducting electron-positron vacuum state. The Landau-Ginzburg model shows that Wilson loops determine phases of two Higgs fields forming superconducting vacuum state of the modified KN solution, quantum vacuum of the electron-positron pairs. The phases of these Higgs fields correspond to two light-like modes of a classical relativistic ring string. We come to the conclusion that the electron models considered by Israel and López are not complete and must be supplemented by a mirror structure that forms a quantum system consistent with QED.

Spin-charge induced spontaneous scalarization of Kerr-Newman black holes

We investigate the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with a positive coupling parameter $\alpha$. This corresponds to exploring the onset of spontaneous scalarization for KN black holes. For this purpose, we use the hyperboloidal foliation method (HFM) to solve the linearized scalar equation numerically. We obtain a 3D graph [$\log_{10}\alpha(a,Q)$] which indicates the onset surface for spontaneous scalarization of KN black holes in the EMS theory. We find that there is no lower bound on the rotational parameter $a$, but its upper bound is given by $M^2-Q^2 \ge a^2$. Also, we confirm that the high rotation enhances spontaneous scalarization of KN black holes in the EMS theory.

Instability of the charged massive scalar field on the Kerr–Newman black hole spacetime

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. Finally, we apply the obtained results to compute the characteristic times of growth and decay of bosonic particles around a supermassive black hole situated at the center of the M87 galaxy.

The effect of the WGC condition on the maximal energy extracted from black holes

In this paper, we study the Penrose process and the maximum energy extracted from the collision of two particles near the Kerr–Newman black hole with WGC condition. We show that these conditions increase the energy extracted from the black hole. In this process, two particles collide in the ergosphere region, leading to two more scattered particles. The fate of these particles leads to falling into a black hole or escaping to infinity. The WGC condition leads to an increase in the energy of the particles escaping to infinity. We also investigated the amount of energy extracted by particles with different spins from the black hole. These achievements will help identify and study other black holes and spinning particles in astrophysics and make how black holes work more transparent in WGC conditions.

Turning rotating D-branes and black holes inside out their photon-halo

We extend our investigation on Couch-Torrence conformal inversions of black holes (BHs) and D-branes in various directions. We analyze asymptotically flat rotating charged BHs in $D=4$, in particular extremal rotating BHs in STU supergravity, and find invariance for special choices of the charges. Due to the dependence of the critical radii on the impact parameter(s), the relation between the scattering angle for geodesics outside the photon-halo and the inspiraling angle for geodesics inside the photon-halo is modified by the inclusion of a boundary term. We also consider rotating BHs in $D=5$ and rotating D3-branes and find invariance under generalized Couch-Torrence inversions for special choices of the angular momenta. Alas we don't find any similar symmetry for smooth horizonless geometries. Moreover, relying on the surprising connection between classical BH perturbation theory and quantum Seiberg-Witten curves for $\mathcal{N}=2$ SYM theories, we study scalar wave equations in these backgrounds and identify the near superradiant modes produced in near-extremal BH mergers. Finally, we study scalar fluctuations around Kerr-Newman BHs in ${\mathrm{AdS}}_{4}$ and find stringent conditions for generalized Couch-Torrence symmetry that are relaxed in the extremal case or by allowing a rescaling of the wave function.

Phase transition and quantum corrections of quintessential Kerr–Newman black hole with cloud of strings

The purpose of this manuscript is to inspecting the phase transition and the critical phenomenon of charged quintessential Kerr-Newman-anti-de Sitter black hole with cloud of strings. In this regard, we evaluate the thermodynamic factors (Hawking temperature, angular momentum and entropy) in the framework of extended phase space. These factors fulfill the Smarr-Gibbs-Dehum equation in the existence of quintessence and cloud of strings. The critical behavior of thermodynamic factors is discussed via two techniques such as Maxwell equal-area law and Van-der Waal like equation of state . It is obtained that the former one is more effective to observe the critical nature of the complex black holes. Further, we study the phase diagram in T − S plane using equal-area law and obtain an isobar depicting the coexistence era of two phases. It is concluded that black holes lower than the critical temperature exhibit the phase transition same as that of Van-der Waal fluid. At the end, we analyze the influence of thermal variations on the black hole’s stability. • We inspect the critical phenomenon of quintessential string Kerr-Newman-AdS BH. • The critical behavior via Maxwell equal-area law and Van-der Waal EoS is studied. • Below the critical temperature, BHs show the VdW fluid like phase transition. • At the end, we analyze the influence of thermal variations on the black hole’s stability.

Weak gravity conjecture from conformal field theory: a challenge from hyperscaling violating and Kerr-Newman-AdS black holes

We search for a possible relationship between weak gravity conjecture (WGC) and conformal field theory (CFT) in hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems using the correlation function introduced in CFT and discuss WGC conditions using the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions , , and , we link WGC to hyperscaling violating black holes owing to the existence of values larger and smaller than one. For the second black hole system, we study the conditions of WGC for Kerr-Newman-AdS black holes using rotation and radius parameters. Then, we show that the conditions of WGC are satisfied when the charged particle near the hyperscaling violating and Kerr-Newman black holes is with a ratio .

Gedanken experiments at high-order approximations: Kerr-Newman black hole cannot be overcharged and overspun

The weak cosmic censorship conjecture (WCCC) of black holes is a fundamental hypothesis in general relativity. The proof of this hypothesis has become a frontier issue in the study of gravity. Recently, Sorce and Wald proposed a new version of the gedanken experiment and examined that the WCCC of Kerr-Newman (KN) black holes is valid under the second-order approximation of the matter fields perturbation. But it is not enough to study the WCCC under the second-order approximation because there is an additional condition that makes the validity of the hypothesis impossible to judge in this case. Therefore, the higher-order approximation of the perturbation process should be further considered to examine the conjecture strictly. Based on the new version of the gedanken experiment, from the two assumptions that the spacetime geometry satisfies the stability condition and that the matter fields should obey the null energy condition, we deduce the $n$th-order perturbation inequality and demonstrate that the event horizon of KN black holes always exists under the $n$th-order approximation of the matter fields perturbation. It indicates that the hypothesis is always satisfied under the arbitrary high-order approximation and also shows that the WCCC of KN black holes has been examined rigorously at the perturbation level.

The dark (BPS) side of thermodynamics in Minkowski4

We explore the BPS limit of asymptotically flat black hole thermodynamics, drawing analogies with recent studies of black holes in anti-de Sitter space. Although ultimately motivated by supersymmetry and quantum gravity, the BPS limit is classically well-defined for the dyonic Kerr-Newman black holes in pure Einstein-Maxwell theory and various generalizations with additional scalars and gauge fields that admit embedding in mathcal{N} = 2 supergravity (for concreteness we consider the STU model). This limit is manifestly different from extremality as it includes a family of rotating Euclidean saddles that represent a (fictitious) thermal branch, smoothly connected with the extremal static Reissner-Nordström black hole and its generalizations with extra matter. We are able to evaluate unambiguously all BPS chemical potentials, finding constant imaginary angular velocity as a consequence of Wick rotation. In the mixed ensemble of fixed magnetic and varying electric charges, we derive the OSV formula that is crucial for the microscopic understanding of the system, and provide evidence that it should be interpreted as a fixed-point formula.

Multi-level images around Kerr–Newman black holes

We study the lensing effects of Kerr–Newman (KN) black holes and the multi-level images of luminous sources around the black holes. We obtain the analytic forms of the lens equations in KN spacetime and derive approximately their limiting forms for photon emissions near the bounded photon orbits. After deriving the expressions of three key parameters γ, δ and τ, we investigate the primary, the secondary and the higher-order images of spherical sources and equatorial disk-like sources. In particular, we find that the charge of KN black hole has a significant effect on the higher-order images.

Modified Hawking temperature of Kerr–Newman black hole in Lorentz symmetry violation theory

In this paper, we study the quantum tunneling of scalar particles near the event horizon of Kerr–Newman black hole under Lorentz violation theory. First, the modified Hamilton–Jacobi equation under Lorentz violation theory in the curved spacetime is reviewed. The modified Hawking temperatures, heat capacities and entropies of Kerr–Newman black hole in frame dragging coordinates and Eddington coordinate are derived. The modified Hawking temperature, heat capacity and change in Bekenstein–Hawking entropy of Kerr–Newman black hole are found to be modified due to Lorentz violation theory and they depend not only on Lorentz violation parameter [Formula: see text] but also on ether-like vector [Formula: see text].

Photon regions, shadow observables, and constraints from M87* of a charged rotating black hole

Inspired by the observations of supermassive black hole M87* in \emph{Event Horizon Telescope }(EHT) experiment, a remarkable surge in black hole physics is to use the black hole shadow's observables to distinguish general relativity (GR) and modified theories of gravity (MoG), which could also help to disclose the astrophysical nature of the center black hole in EHT observation. In this paper, we shall extensively carry out the study of a charged rotating black hole in conformal gravity, in which the term related with the charge has different falloffs from the usual Kerr-Newman (KN) black hole. We investigate the spacetime properties including the horizons, ergospheres and the photon regions; afterward, we show the boundary of black hole shadow and investigate its characterized observables. The features closely depend on the spin and charge parameters, which are compared with those in Kerr and KN black holes. Then presupposing the M87* a charged rotating black hole in conformal gravity, we also constrain the black hole parameters via the observation constraints from EHT experiment. We find that the constraints on the inferred circularity deviation, $\Delta C \lesssim 0.1$, and on the shadow axial ratio, $1< D_x \lesssim 4/3$, for the M87* black hole are satisfied for the entire parameter space of the charged rotating black hole in conformal gravity. However, the shadow angular diameter $\theta_d = 42 \pm 3 \mu as$ will give upper bound on the parameter space. Our findings indicate that the current charged rotating black hole in conformal gravity could be a candidate for astrophysical black holes. Moreover, the EHT observation on the axial ratio $D_x$ may help us to distinguish Kerr black hole and the current charged rotating black hole in conformal gravity in some parameter space.

The Average Radial Speed of Light From Near to Far Space Surrounding the Kerr–Newman Super-Gravitational Source

The Kerr–Newman metric is used to discuss the average radial speed of light from near to far space surrounding the super-gravitational source like a black hole which can be observed by a weak-gravitational reference frame such as an observer on the Earth. The velocity equation of light near the black hole is represented by the Boyer–Lindquist coordinates (t, r, θ, and ϕ), and the main parameters are the Schwarzschild radius RS, the rotation term a, and the charged term RQ. From the calculations, the average radial speed of light from r = RS to r = αRS with α&gt;1 is possibly observed exceeding c by an observer on the Earth. The result can extend to the large r place when the rotation of the black hole is high or the charge is very large. This average radial speed finally approaches c far away from the black hole. We also propose a new explanation based on our results that the observation of the faster-than-light particle is due to the light bending near the Kerr–Newman black hole or supermassive star with very strong gravity. In addition, two superluminal theories used to explain the speed of light in astronomy are compared. One is the Doppler effect in special relativity, and the other is the change in the photon speed due to the QED contribution of one-loop vacuum polarization to the photon effective action. The former seems to mainly appear as the change of the observed wavelength or frequency, while the latter is probably the random and irregular occurrences. Our explanation is based on the Kerr–Newman metric in general relativity, and it extends the discussion from the flat spacetime in special relativity to the curved spacetime which is suitable for many superluminal observations near the super-gravitational sources like the black hole. Our calculations are used to verify tangible observations like the M87 jet.