The Kerr-Newman two-twistor particle
Joon-Hwi Kim
该研究在扭矢粒子理论中构建了克尔-新曼黑洞的全部阶数世界线有效作用，并揭示了自双曲背景中的隐藏对称性。
在扭矢粒子理论中，实现了克尔-新曼黑洞的全部阶数世界线有效作用。在自双曲背景中，精确的隐藏对称性被识别出来。
An all-orders worldline effective action for Kerr-Newman black hole is achieved in twistor particle theory. Exact hidden symmetries are identified in self-dual backgrounds.
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The Kerr two-twistor particle
本文在twistor粒子理论中提出了一种针对克尔黑洞的全阶世界线有效作用量，为黑洞物理研究提供了新的理论工具。
Recently, we introduced the "Newman-Penrose map," a novel correspondence between a certain class of solutions of Einstein's equations and self-dual solutions of the vacuum Maxwell equations, which we showed was closely related to the classical double copy. Here, we give an alternative definition of this correspondence in terms of quantities that are defined naturally on twistor space, and a shear-free null geodesic congruence on Minkowski space whose twistorial character is articulated by the Kerr theorem. The advantage of this reformulation is that it is purely geometrical in nature, being ma…
Kerr-Schild formalism is generalized by incorporation of the Kerr Theorem with polynomials of higher degrees in $Y\in CP^1.$ It leads to multisheeted twistor spaces and multiparticle solutions.
Nonexistence of Majorana fermions in Kerr-Newman type spacetimes with nontrivial charge
本文通过分离 Kerr-Newman 及 Kerr-Newman-(A)dS 时空中时间周期 Majorana 费米子的 Dirac 方程，利用两个代数恒等式证明非零电荷或磁荷时相应视界区域内不存在可微时间周期解。
The Kerr theorem is revisited as part of the twistor program in six dimensions. The relationship between pure spinors and integrable 3-planes is investigated. The real condition for Lorentzian spacetimes is seen to induce a projective property in the space of solutions, reminiscent of the quaternionic structure of the 6-dimensional Lorentz group. The twistor equation (or Killing spinor equations generically) also has an interpretation as integrable null planes and a family of Einstein spacetimes with this property are presented in the Kerr-Schild fashion.
Rigidity of the extremal Kerr-Newman horizon
本文证明四维爱因斯坦-麦克斯韦理论（含宇宙学常数）中极端视界紧致横截面内禀几何需允许基灵向量场或静态，据此完成近视界几何分类并确定其必为极端克尔-纽曼视界。
The Kerr-Newman spinning particle displays some remarkable relations to the Dirac electron and has a reach spinor structure which is based on a twistorial description of the Kerr congruence determined by the Kerr theorem. We consider the relation between this spinor-twistorial structure and spinors of the Dirac equation, and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the twistorial structure of Kerr geometry. As a result, the Dirac electron acquires an extended space-time structure having clear coordinate description w…
Kerr-Schild (KS) geometry of the rotating black-holes and spinning particles is based on the associated with Kerr theorem twistor structure which is defined by an analytic curve $F(Z)=0$ in the projective twistor space $Z \in CP^3 .$ On the other hand, there is a complex Newman representation which describes the source of Kerr-Newman solution as a "particle" propagating along a complex world-line $X(\t)\in CM^4,$ and this world-line determines the parameters of the Kerr generating function $F(Z).$ The complex world line is really a world-sheet, $\t= t + i σ,$ and the Kerr source may be conside…
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.
Kerr-Schild (KS) geometry is based on a congruence of twistor null lines which forms a holographic space-time determined by the Kerr theorem. We describe in details integration of the non-stationary Debney-Kerr-Schild equations for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact KS solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. These twistor-beam pulses have very strong back reaction to metric and BH horizon and produce a fluctuating holographic KS geometry which takes…
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 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.
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.
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors. This is followed by a description of an asymptotic version of the Kerr theorem that produces regular asymptotically shear free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes.
Exact Kerr-Schild (KS) solutions for electromagnetic excitations of black-holes, have the form of singular beams supported on twistor lines of the KS geometry. These beams have a very strong back-reaction on the metric and horizon and create a fluctuating KS geometry occupying an intermediate position between the classical and quantum gravities. We consider the Kerr theorem, which determines the twistor structure of the KS geometry and the corresponding holographic prequantum space-time adapted to subsequent quantum treatment.
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…
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the expectation that the family of extreme Kerr-Newman black-holes is unstable. It remains of course to be seen whether the whole family of charged black-holes, including those extremes, is stable or not.
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.
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 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.
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…
The Kerr spinning particle has a remarkable analytical twistorial structure. Analyzing electromagnetic excitations of the Kerr circular string which are aligned to this structure, we obtain a simple stringy skeleton of the spinning particle which is formed by a topological coupling of the Kerr circular singular string and by an axial singular stringy system. We show that the chiral traveling waves, related to an orientifold world-sheet of the axial stringy system, are described by the massive Dirac equation, so we argue that the axial string may play the part of a stringy carrier of wave funct…
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 show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordström-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the non-linear stability of the Kerr-Newman-de Sitter family of black holes for small angular momenta, recently established by the author, together with an extension argument for Killing vector fields. Our black hole uniqueness result only requires the solution to have high but finite regularity; in particular, we do not make any analyticity assumptions.
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…
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…
We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from horizons. We study the interaction of geodesics with special features of the metric, particularly regions of angular degeneracy or "theta horizons" in the de Sitter case. Finally, we characterize a number of stable equilibrium orbits.
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 that a stationary asymptotically flat electro-vacuum solution of Einstein's equations that is everywhere locally "almost isometric" to a Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. In particular this implies that the assumption of a single event horizon in Alexakis-Ionescu-Klainerman's proof of perturbative uniqueness of Kerr black holes is in fact unnecessary.
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,…
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…
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 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.
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.
Newman-Janis Algorithm from Taub-NUT Instantons
本文展示Kerr度规是自对偶与反自对偶Taub-NUT瞬间子的非线性叠加，推动Newman-Janis算法成为具有明确物理起源的Kerr度规推导方法。
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 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.
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.
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…
We present a new twisted rotating black hole solution by performing Demia{ń}ski-Newman-Janis algorithm to the electrically and dyonically charged black hole with quintessence in Rastall theory of gravity. Using our black hole solution, we argue that Rastall gravity is not equivalent with Einstein gravity. For further explanation, the black hole properties such as the horizon and ergosphere are studied for which there are some different properties for those theories. Some thermodynamic properties of the black hole solution are also discussed. At the end, considering the Kerr/CFT correspondence …
This article explores the characteristics of ergoregion, horizons and circular geodesics around a Kerr-Newman-Kasuya black hole. We investigate the effect of spin and dyonic charge parameters on ergoregion, event horizon and static limit surface of the said black hole. We observed that both electric, as well as magnetic charge parameters, results in decreasing the radii of event horizon and static limit, whereas increasing the area of ergoregion. The obtained results are compared with that acquired from Kerr and Schwarzschild black holes. Moreover, we figured out the photons orbit of circular …
We obtain a global embedding of the surface of a rapidly rotating Kerr-Newman black hole in an Euclidean 4-dimensional space.
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