Kerr-Newman Research Articles

The shadows of accelerating Kerr-Newman black hole and constraints from M87*

In this paper, we study the influence of the parameters for the accelerating Kerr-Newman black hole on the shadows and the constraints, extensively. We find that the rotating parameter a, the charge parameter e, and the inclination angle θ0 affect the shadow qualitatively similar to that of Kerr-Newman black holes. The result shows that the size of the shadow will scale down with the accelerating factor A. Besides, the factor A also can affect the best viewing angles, which make the observations maximum deviate from θ0=π2, and the degree of the deviations are less than 1%. Then, we assume the M87* as an accelerating Kerr-Newman black hole with the mass M=6.5×109M⊙ and the distance r0=16.8Mpc. Combining the EHT observations, we find that neither the observations, circularity deviation ΔC or axial ratio Dx can distinguish the accelerating black hole or not. However, the characteristic areal-radius of the shadow curve Ra can give corresponding constraints on the parameters of the accelerating Kerr-Newman black hole. The result shows that the bigger accelerating factor A is, the stronger constraints on the rotating parameter a and charged parameter e. The maximum range of the accelerating factor is Ar0≤0.558 for a accelerating Schwarzschild case with (a/M=e/M=0), and for an extremely slow accelerating case (Ar0≤0.01), the ranges of rotating parameter a and charged parameter e are a/M∈(0,1) and e/M∈(0,0.9).

Explicit black hole thermodynamics in natural variables

We consider the general thermal asymptotically flat Kerr-Newman black holes in 4d Einstein-Maxwell theory. Even though their thermodynamics has been understood for decades, the Gibbs free energy and on-shell action are only known implicitly as functions of the standard chemical potentials. Using the so-called left and right moving (or holomorphic and anti-holomorphic) variables related to the chemical potentials on both the outer and the inner horizons, we are able to present explicit and very simple expressions for all quantities. We discuss various limits in the parameter space, remarkably finding a smooth BPS limit allowing direct access to the extremal surface. In the BPS limit the anti-holomorphic part of the on-shell action vanishes identically, leading automatically to the holomorphic expression expected microscopically. This gives us confidence that the newly defined thermal partition function in terms of these variables is the natural candidate for a full microscopic description.

Energy extraction, or lack thereof

The problem of stability of rotating black holes is the subject of a long standing research program since the 1960s and remains an unresolved problem in general relativity. A major obstacle in the black hole stability problem is that the energy of waves propagating through rotating black holes spacetimes is not necessarily positive-definite, due to the so called ergo-region. This is a serious complication that limits the efficacy of most mathematical techniques. In this expository article, we report that, despite the ergo-region, there exists a positive-definite total energy for axisymmetric Maxwell, gravitational and electrovacuum perturbations of Kerr and Kerr–Newman black hole spacetimes.

Kerr-Newman black holes from \U0001d4a9 = 1∗

The microstate counting of charged rotating AdS5 supersymmetric black holes has been reformulated in terms of an extremization problem, obtained from the superconformal index of the 4d dual SCFT. On the gravitational side this problem corresponds to the attractor mechanism of the theory KK reduced on AdS4. Such procedure has indeed been successfully applied to some consistent truncations with a known field theory dual description. In this paper we study the case of the Leigh-Strassler fixed point along these lines, finding an agreement between the field theory and the gravitational results.

Holographic thermodynamics of rotating black holes

We provide mass/energy formulas for the extended thermodynamics, mixed thermodynamics, and holographic conformal field theory (CFT) thermodynamics for the charged and rotating Kerr-Newman Anti-de Sitter black holes. Then for the CFT thermal states dual to the black hole, we find the first-order phase transitions and criticality phenomena in the canonical ensemble with fixed angular momentum, volume, and central charge. We observe that the CFT states cannot be analogous to the Van der Waals fluids, despite the critical exponents falling into the universality class predicted by the mean field theory. Additionally, we examine the (de)confinement phase transitions within the grand canonical ensemble with fixed angular velocity, volume, and central charge of the CFT. Our findings suggest that the near zero temperature (de)confinement phase transitions can occur with the angular velocity of the CFT that solely depends on the CFT volume.

Loop quantum gravity and quasinormal mode of Kerr–Newman black hole

Taking the advantages of loop quantum gravity (LQG), the quasinormal mode frequency spectrum of black holes is studied with the first law of thermodynamics of black holes by calculating the tunneling rate. With the minimum event horizon area interval given by LQG, our results show that one group of the quasinormal mode spectrum for Kerr–Newman black hole depends only on the outer horizon parameters of the black hole. Choosing the minimum spin properly, we derive the quasinormal mode completely consistent with the present results. More importantly, our results show that the quasinormal modes of black holes should have a series of separated frequency spectra, which further proves that the space-time of black holes is quantized.

Compactifying the Kerr-Schild double copy

We show that the classical double copy relationship for Kerr-Schild spacetimes can be dimensionally reduced to give a natural notion of the double copy for Kaluza-Klein theory with gravity coupled to a gauge field and a dilaton. Under dimensional reduction the Kerr-Schild (KS) ansatz becomes the stringy Kerr-Schild (sKS) ansatz introduced by Wu. This ansatz captures many Kaluza-Klein black hole solutions, including single-charge black holes arising in both gauged and ungauged supergravity theories. We identify the single copy gauge field and scalar field of an arbitrary sKS solution. We show that the boost-reduction procedure for generating charged black hole solutions can be generalized to any stationary KS seed, and used to combine the metric with the zeroth and single copies of that seed into a single sKS solution. Furthermore, we comment on multi-charge solutions that can be written in a multi-sKS form, proposing a double copy interpretation involving multiple single copy sectors.

Geometry, conformal Killing-Yano tensors and conserved “currents”

In this paper we discuss the construction of conserved tensors (currents) involving conformal Killing-Yano tensors (CKYTs), generalising the corresponding constructions for Killing-Yano tensors (KYTs). As a useful preparation for this, but also of intrinsic interest, we derive identities relating CKYTs and geometric quantities. The behaviour of CKYTs under conformal transformations is also given, correcting formulae in the literature. We then use the identities derived to construct covariantly conserved “currents”. We find several new CKYT currents and also include a known one by Penrose which shows that “trivial” currents are also useful. We further find that rank-n currents based on rank-n CKYTs k must have a simple form in terms of dk. By construction, these currents are covariant under a general conformal rescaling of the metric. How currents lead to conserved charges is then illustrated using the Kerr-Newman and the C-metric in four dimensions. Separately, we study a rank-1 current, construct its charge and discuss its relation to the recently constructed Cotton current for the Kerr-Newman black hole.

Particle motion in the Einstein-Euler-Heisenberg rotating black hole spacetime

We study the motion of charged test particles and photons in the gravitational field of the rotating electrically charged Einstein-Euler-Heisenberg black hole solution. This describes a nonlinear electromagnetic generalization of the Kerr-Newman solution, which endows the vacuum with an effective dielectric constant. The orbits of photons are analyzed by means of the effective Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski pseudometric related to the geometrical metric and to the electromagnetic energy-momentum tensor. The QED induced modifications of the shape of the shadow are presented and discussed.

Quasinormal modes of slowly rotating Kerr-Newman black holes using the double series method

We calculate the spectrum of quasinormal modes of slowly rotating Kerr-Newman black holes. Using a perturbative double expansion method, second order in rotation and first order in non-radial perturbations, we obtain the system of equations that describe polar-led and axial-led perturbations. We analyse gravitational, electromagnetic and scalar fundamental modes, focusing on the $\mathrm{l}=2$ perturbations. We reproduce previous results and check that isospectrality between axial and polar-led perturbations is approximately satisfied with good accuracy. Our results show that the slow rotation approximation can be used to estimate with reasonable precision the spectrum of configurations up to 50-60$\%$ of the extremal angular momentum.

Phase transitions and thermodynamic geometry of a Kerr–Newman black hole in a cavity

Phase transitions and thermodynamic geometry of a Kerr–Newman black hole in a cavity

Spectral stability of near-extremal spacetimes

It has been suggested that the spectrum of quasinormal modes of rotating black holes is unstable against additional potential terms in the perturbation equation, as the operator associated with the equation is non-self-adjoint. We point out that a bilinear form has been constructed previously to allow a perturbation analysis of the spectrum, which was applied to study the quasinormal modes of weakly charged Kerr-Newman black holes [Phys. Rev. D 91, 044025 (2015)]. The proposed spectral instability should be restated as instability against potential terms that have an infinitesimal ``energy'' norm that is specifically defined by the type of inner products introduced by Jaramillo et al. and preserving the physical meaning of energy. We argue that it is necessary to address the stability of all previous mode analysis results to reveal their susceptibility to energetically infinitesimal perturbations. In particular, for near-extremal Kerr spacetime, we show that the spectrum of zero-damping modes, which have slow decay rates, is unstable (with order unity fractional change in decay rates) with fine-tuned modification of the potential. The decay rates are, however, always positive with energetically infinitesimal perturbations. If finite potential modifications are allowed near the black hole, it is possible to find superradiantly unstable modes, i.e., a ``black hole bomb'' without an explicit outer shell. For the zero-damping modes in near-extremal Reissner-Nordstr\"om--de Sitter black holes, which are relevant for the breakdown of strong cosmic censorship, we find that the corresponding spectrum is stable under energetically infinitesimal perturbations.

Next-to-leading-order solution to Kerr-Newman black hole superradiance

The superradiant instabilities of Kerr-Newman black holes with charged or uncharged massive spin-0 fields are calculated analytically to the next-to-leading order in the limit of $\alpha\sim r_g \mu \ll 1$. A missing factor of $1/2$ in the previous leading-order result is identified. The next-to-leading order result has a compact form and is in good agreement with existing numerical calculations. The percentage error increases with $\alpha$, from a few percent for $\alpha\sim 0.1$ to about $50\%$ for $\alpha\sim 0.4$. Massive neutral scalars too heavy to be produced with Kerr black hole superradiance may exist in the superradiant region of Kerr-Newman black holes.

Dyon production from near-extremal Kerr–Newman–(anti-)de Sitter black holes

Using the enhanced symmetry in the near-horizon region of the near-extremal dyonic Kerr–Newman (KN) black hole in the (A)dS space, we find the exact solutions for dyonic charged scalar field in terms of the hypergeometric function and explicitly compute the Schwinger effect for the emission of electric and/or magnetic charges. The emission formula confirms a universal factorization of the Schwinger formula in the AdS_2 and another Schwinger formula in the two-dimensional Rindler space determined by the effective temperature and the Hawking temperature with the chemical potentials of electric and/or magnetic charges and the angular momentum. The emission of the same species of charges from the KN black hole is enhanced in the AdS boundary while it is suppressed in the dS boundary. In addition, the dragging of particles in the KN black hole diminishes the emission of charges in both AdS and dS spaces. The AdS geometry of near-horizon gives the Breitenloher–Freedman (BF) bound, within which the stability of dyonic KN black holes is guaranteed against both the emission of charges and Hawking radiation.

Equations-of-state deduced form different types of black holes

Black holes are seen as thermodynamical systems. They can be characterized by thermodynamic intensive quantities such as temperature, pressure, and extensive quantities such as entropy and energy density. In this paper, we focus on the thermodynamical properties of (a) Schwarzschild, (b) Reissner–Nordström, (c) Kerr, and (d) Kerr–Newman black holes. These allow to estimate the corresponding equations-of-state (EoS) and the squared speed of sound for each of them. The latter helps to calculate the ratio of the bulk viscosity to the shear viscosity for each of the black holes. We conclude that the resulting EoS enhances when moving from Schwarzschild to Reissner–Nordström to Kerr, and to Kerr–Newman black holes.

Dyonic black holes in the theory of two electromagnetic potentials. II

The results obtained in our previous paper are now extended to the case of stationary axially symmetric dyonic black boles within the theory of two electromagnetic potentials. We slightly enlarge the classical Ernst formalism by introducing, with the aid of the $t$- and $\varphi$-components of the dual potential $B_\mu$, the magnetic potential $\Phi_m$ which, similar to the known electric potential $\Phi_e$, also takes constant value on the black hole horizon. We analyze in detail the case of the dyonic Kerr-Newman black hole and show how the Komar mass must be evaluated correctly in this stationary dyonic model. In particular, we rigorously prove the validity of the standard Tomimatsu mass formula and point out that attempts to "improve" it made in recent years are explained by misunderstanding of the auxiliary role that singular potentials play in the description of magnetic charges. Our approach is symmetrical with respect to electric and magnetic charges and, like in the static case considered earlier, Dirac strings of all kind are excluded from the physical picture of the stationary black hole dyonic spacetimes.

Radii of spherical photon orbits around Kerr-Newman black holes

The spherical photon orbits around a black hole with constant radii are particular important in astrophysical observations of the black hole. In this paper, the equatorial and non-equatorial spherical photon orbits around Kerr-Newman black holes are studied. The radii of these orbits satisfy a sextic polynomial equation with three parameters, the rotation parameter $u$, charge parameter $w$ and effective inclination angle $v$. It is found that there are two polar orbits and one is inside and the other is outside the event horizon. For orbits in the equatorial plane around an extremal Kerr-Newman black hole , we find three positive solutions to the equation and provide analytical formulas for the radii of the three orbits. It is also found that a critical value of rotation parameter $u=\frac{1}{4}$ exists, above which only one retrograde orbit exists outside the event horizon and below which two orbits (one prograde and one retrograde) exist outside the event horizon. For orbits in the equatorial plane of a nonextremal Kerr-Newman black hole, there are four or two positive solutions. A critical curve in $(u,w)$-plane which separates the regions is also found. On this critical curve, the explicit formulas of three solutions are found. There always exist two equatorial photon orbits outside the event horizon in this case. For orbits between the above two special planes, there are four or two solutions to the general sextic equation. When the black hole is extremal, it is found that there is a critical inclination angle $v_{cr}$, below which only one orbit exists and above which two orbits exist outside the event horizon for a rapidly rotating black hole $u>\frac{1}{4}$. At this critical inclination angle, exact formula for the radii is also derived. Finally, a critical surface in parameter space of ($u,w,v$) is shown that separates regions with four or two solutions.

On the discrete version of the Kerr–Newman solution

This paper continues our work on black holes in the framework of the Regge calculus, where the discrete version (with a certain edge length scale [Formula: see text] proportional to the Planck scale) of the classical solution emerges as an optimal starting point for the perturbative expansion after functional integration over the connection, with the singularity resolved. An interest in the present discrete Kerr–Newman-type solution (with the parameter [Formula: see text]) may be to check the classical prediction that the electromagnetic contribution to the metric and curvature on the singularity ring is (infinitely) greater than the contribution of the [Formula: see text]-function-like mass distribution, no matter how small the electric charge is. Here, we encounter a kind of a discrete diagram technique, but with three-dimensional (static) diagrams and with only a few diagrams, although with modified (extended to complex coordinates) propagators. The metric (curvature) in the vicinity of the former singularity ring is considered. The electromagnetic contribution does indeed have a relative factor that is infinite at [Formula: see text], but, taking into account some existing estimates of the upper bound on the electric charge of known substances, it is not so large for habitual bodies and can only be significant for practically nonrotating black holes.

On the Radial Solutions of the Dirac Equation in the Kerr-Newman Black Hole Surrounded by a Cloud of Strings

In this paper, we obtain the metric of the space-time generated by a charged and rotating gravitational body surrounded by a loud of strings, namely, the Kerr–Newman black hole space-time with the addition of a cloud of strings. In this background, we find the radial solutions of the Dirac equation for massive particles and show that they are given in terms of the Generalized Heun functions. The dependence of these solutions on the parameter that codifies the presence of the cloud of strings is pointed out.

Curvature induced scalarization of Kerr-Newman black hole spacetimes

With certain nonminimal coupling between a massless scalar field and the Gauss-Bonnet curvature invariant in the extended scalar-tensor-Gauss-Bonnet (ESTGB) field theory, tachyonic instability of the Kerr-Newman (KN) black hole is promoted. Critical spin and charge for the onset of the spontaneous scalarization phenomenon for the KN black hole are calculated in the infinitely large coupling limit. Then the analytical formula for the coupling-strength-dependent critical existence line is obtained for the black-hole-scalar-field configuration in a finite large coupling regime. Moreover, numerical methods are used to perform threshold curves that are boundaries between bald KN black holes and their hairy counterparts. Intriguingly, we get to know the KN black hole can be scalarized in the vanishing spin limit in ESTGB theory.