Jacek Jezierski, Tomasz Smołka
We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Kiling tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We present a new solution in Einstein-Maxwell theory which can be considered as the magnetized version of Kerr-Taub-NUT solution. Some properties of the spacetime are discussed. We also compute the entropy of extremal black hole in the spacetime by using the Kerr/CFT correspondence approach.
Static magnetic dipole solutions of Einstein-Maxwell equations from the soliton solutions of a Kerr object
The spacetime of a boosted Bondi-Sachs rotating black hole is considered as a proper background to examine electromagnetic configurations connected to analytic solutions of Maxwell equations. In our analysis, we first use the Bondi-Sachs transformations in order to bring the boosted rotating black hole metric into the Kerr-Schild form, from which zero angular momentum observers (ZAMOs) are constructed via the ADM formalism. In Kerr-Schild coordinates we obtain the Killing fields as sources of Maxwell electrodynamics, and we fix a ZAMO in order to evaluate the components of the electric and mag…
An exact expression derived in the literature for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is reviewed. The exact LT precession frequencies for Kerr, Kerr-Taub-NUT and Taub-NUT spacetimes are explicitly derived. Remarkably, in the case of the zero angular momentum Taub-NUT spacetime, the frame-dragging effect is shown {\it not} to vanish, when considered for spinning test gyroscopes. The result becomes sharper for the case of vanishing ADM mass of that spacetime. We clarify how our results are consistent with claims in the rece…
It is not currently known how to put the Kerr spacetime metric into the so-called Gordon form, although the closely related Kerr-Schild form of the Kerr metric is well known. A Gordon form for the Kerr geometry, if it could be found, would be particularly useful in developing analogue models for the Kerr spacetime, since the Gordon form is explicitly given in terms of the 4-velocity and "refractive index" of an effective medium. In the current article we report progress toward this goal. First we present the Gordon form for an approximation to Kerr spacetime in the slow-rotation limit, obtaine…
We study Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell's field. We prove that these metrics linearize and simplify the field equations of generic gravity theories with Maxwell's field.
In this paper, we consider the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with nonminimal negative scalar coupling to Maxwell term, and then obtain a bound $(\frac{a}{r_+}\geq0.4142)$ for spin parameter $a$ of KN black hole in the limit of coupling constant $α\rightarrow-\infty$ by using analytical method. In addition, we perform a $(2+1)$-dimensional time evolution of linearized scalar field perturbation on the KN black hole background by implementing the hyperboloidal foliation method numerically in the EMS theory. It recovers the \texti…
Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked-singularity spacetimes, and their relevance for thin accretion discs is established.
The static Kottler metric is the Schwarzschild vacuum metric extended to include a cosmological constant. Angular momentum is added to the Kottler metric by using Newman and Janis' complexifying algorithm. The new metric is the Lambda generalization of the Kerr spacetime. It is stationary, axially symmetric, Petrov type II, and has Kerr-Schild form.
Time-domain analysis of scalar perturbations of Kerr--Newman black holes with Chern--Simons and Maxwell couplings
本文通过线性标量扰动分析Kerr--Newman黑洞在Chern--Simons和Maxwell耦合下的标量化阈值，发现不同耦合参数下阈值分支的合并行为。
The astrophysical importance of the Kerr spacetime cannot be overstated. Of the currently known exact solutions to the Einstein field equations, the Kerr spacetime stands out in terms of its direct applicability to describing astronomical black hole candidates. In counterpoint, purely mathematically, there is an old classical result of differential geometry, due to Darboux, that all 3-manifolds can have their metrics recast into diagonal form. In the case of the Kerr spacetime the Boyer-Lindquist coordinates provide an explicit example of a diagonal spatial 3-metric. Unfortunately, as we demon…
We focus on the method recently proposed by Lunin and Frolov-Krtouš-Kubizňák to solve the Maxwell equation on the Kerr-NUT-(A)dS spacetime by separation of variables. In their method, it is crucial that the background spacetime has hidden symmetries because they generate commuting symmetry operators with which the separation of variables can be achieved. In this work we reproduce these commuting symmetry operators in a covariant fashion. We first review the procedure known as the Eisenhart-Duval lift to construct commuting symmetry operators for given equations of motion. Then we apply this pr…
Using the energy momentum complex given by Møller in 1978 based on the absolute parallelism, the energy distribution in Kerr spacetime is evaluated. The energy with this spacetime is found to be the same as it was earlier evaluated using different definitions mainly based on the metric tensor.
We provide a prescription to solve the metric completion problem in gravitational self-force calculations on a Kerr spacetime by fixing the remaining gauge freedom. We discuss the explicit example of eccentric equatorial orbits, recovering all limiting cases already studied in the literature of eccentric orbits in Schwarzschild as well as circular orbits in both Schwarzschild and Kerr spacetimes.
We prove, outside the influence region of a ball of radius $R_0$ centered in the origin of the initial data hypersurface, the existence of global solutions near to Kerr spacetime, provided that the initial data are sufficiently near to those of Kerr; This external region is the "far" part of the outer region of the perturbed Kerr spacetime. Moreover if we assume that the corrections to the Kerr metric decay sufficiently fast, $o(r^{-3})$, we prove that the various null components of the Riemann tensor decay in agreement with the "Peeling theorem".
We will show that the Nariai metric, i.e. the static spherically symmetric vacuum spacetime with a cosmological constant, admits a conformally Kerr-Schild spacetime representation. We find the vacuum solutions of the Einstein-Maxwell equations for the Nariai metric using the Horsky-Mitskievich generating conjecture.
The Kerr spacetime is perhaps the most astrophysically important of the currently known exact solutions to the Einstein field equations. Whenever spacetimes can be put in unit-lapse form it becomes possible to identify some very straightforward timelike geodesics, (the "rain" geodesics), making the physical interpretation of these spacetimes particularly clean and elegant. The most well-known of these unit-lapse formulations is the Painleve-Gullstrand form of the Schwarzschild spacetime, though there is also a Painleve-Gullstrand form of the Lense-Thirring (slow rotation) spacetime. More radic…
A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this construction works for the Kerr spacetime.
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.
We obtain a characterization of the Kerr metric among stationary, asymptotically flat, vacuum spacetimes, which extends the characterization in terms of the Simon tensor (defined only in the manifold of trajectories) to the whole spacetime. More precisely, we define a three index tensor on any spacetime with a Killing field, which vanishes identically for Kerr and which coincides in the strictly stationary region with the Simon tensor when projected down into the manifold of trajectories. We prove that a stationary asymptotically flat vacuum spacetime with vanishing spacetime Simon tensor is l…
In this work we study the quasilocal energy as in [11] for a constant radius surface in Kerr spacetime in Boyer-Lindquist coordinates. We show that under suitable conditions for isometric embedding, for a stationary observer the quasilocal energy defined in [11] for constant radius in a Kerr like spacetime is exactly equal to the Brown-York quasilocal energy [2]. By some careful estimations, we show that for a constant radius surface in the Kerr spacetime which is outside the ergosphere the embedding conditions for the previous result are satisfied. We discuss extremal solutions as described i…
In this article we study the innermost stable circular orbit (ISCO) of electrically charged particles in the electrically charged Reissner-Nordström spacetime, the Kerr-Newman spacetime and the Kerr-Sen spacetime. We find that the radius of the ISCO increases with an increasing particle-black hole charge product $|qQ|$ in the case of attractive Coulomb interaction $qQ<0$. For repulsive Coulomb interaction, the ISCO radius first decreases to a minimum and then increases again, until it diverges as the charge product approaches one. If the charge $Q$ of the black hole is very small, the minimum …
We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general relativistic initial data sets with asymptotically Kerr-de Sitter ends. The corresponding Hamiltonians are calculated. Some implications for black-hole thermodynamics are pointed out.
Trapped photon region in the phase space of sub-extremal Kerr-Newman and Kerr-Sen spacetimes
本文研究了 Kerr-Newman 和 Kerr-Sen 空间时域中捕获光子区域的几何和拓扑结构，证明其投影具有特定拓扑结构。
We show that the~braneworld rotating Kerr--Newman black hole and naked singularity spacetimes with both positive and negative braneworld tidal charge parameter can be separated into fourteen classes according to properties of circular geodesics governing the~Keplerian accretion. We determine efficiency of the~Keplerian accretion disks for all braneworld Kerr--Newman spacetimes. We demonstrate occurrence of an~infinitely deep gravitational potential in Kerr--Newman naked singularity spacetimes having the~braneworld dimensionless tidal charge $b \in (1/4,1)$ and the~dimensionless spin $a \in (2\…
Quasi-local mass on rigid or round spheres in Kerr spacetime
本文基于Hamilton方法引入并分析拓扑球面多极展开的准局部质量，并在Kerr时空中对刚性球与圆球两种曲面进行了测试。
In this paper, we investigate Hawking radiation of massive spin-1 particles from 5-dimensional Kerr-Gödel spacetime. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the relativistic Proca equation, we obtain the quantum tunneling rate of the massive vector particles. Using the obtained tunneling rate, we show how one impeccably computes the Hawking temperature of the 5-dimensional Kerr-Gödel spacetime.
Gaussian curvature of the two-surface r=0, t=const is calculated for the Kerr-de Sitter and Kerr-Newman-de Sitter solutions, yielding non-zero analytical expressions for both the cases. The results obtained, on the one hand, exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions.
We find a new class of exact solutions in the Einstein-Maxwell theory by employing the Ernst magnetization process to the Kerr-Newman-Taub-NUT spacetimes. We study the solutions and find that they are regular everywhere. We also find the quasilocal conserved quantities for the spacetimes, the corresponding Smarr formula and the first law of thermodynamics.
A semi-tetrad decomposition of the Kerr spacetime
本文首次将1+1+2协变方法应用于Kerr时空，显式给出能层外几何量及其演化传播方程，突出涡量作用，并修正了早期方程错误。
The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. At first we show that a Kerr-de Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four dimensional spacetime regions contained within Killing horizons or a Killing horizon and the asymptotic de Sitter region. From this perspective and leaving aside topological identifications, the causal properties of a Kerr de Sitter spacetime are determined by the causal properties of the individual Carter's blocks viewed as spacetimes in their own right. We show that an…
We analyze the stability of circular geodesics for timelike as well as null geodesics of the Kerr BH spacetime with rotation parameter on the equatorial plane by Lyapunov stability analysis. Also, we verify the results of stability by presenting the phase portrait for both timelike and null geodesics. Further, by reviewing the Kosambi-Cartan-Chern (KCC) theory, we analyze the Jacobi stability for Kerr spacetime and present a comparative study of the methods used for stability analysis of geodesics.
The second-order post-Newtonian solution for the light propagation in the field of Kerr-Newman black hole is achieved via an iterative method. Based on this result, we further obtain the second-order post-Newtonian light deflection in Kerr-Newman spacetime, which is formulated in an united form for any arbitrarily incident directions. All results are exhibited in the coordinate system constituted by the initial light-direction vector, the impact vector, and their cross-product.
We study the absorption probability and Hawking radiation spectra of a phantom scalar field in the Kerr black hole spacetime. We find that the presence of the negative kinetic energy terms modifies the standard results in the greybody factor, super-radiance and Hawking radiation. Comparing with the usual scalar particle, the phantom scalar emission is enhanced in the black hole spacetime.
It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the special value determined by the Kerr and NUT parameters, and the radius of the horizon, then the corresponding horizon does not suffer that problem. In the current paper, the projectively non-singular horizons are investigated. They are found to be cosmological and non-extremal. Every projectively non-singular horizon can be used to define a global completion o…
We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post- Newtonian expansions for the gauge invariant precession function along circular geodesics valid for arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the GSF-PN results, and the expected lightring divergen…
We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.
We prove that there exists a phase space of canonical variables for the initial value problem for axially symmetric Maxwell fields propagating in Kerr-de Sitter black hole spacetimes such that their motion is restricted to the level sets of a positive-definite Hamiltonian, despite the ergo-region.
A radial deformation of the Kerr metric is studied which leads to the appearance of wormholes in certain cases. {\bf These wormholes can be thought of as being formed by two distinct but identical asymptotically non-flat spacetimes joined at the throat}. The status of energy conditions are discussed in details. The components of the energy-momentum tensor of the spacetime and its eigenvalues are explicitly given. It is shown that the resulting spacetime, represents a family of exact anisotropic fluid solutions.
We have investigated the acceleration of the unbound high energy particles moving along the rotation axis in the Kerr-Taub-NUT spacetime, and then study the dependence of the repulsive effects on the NUT charge for the particles in the spacetime. Whether the repulsive effects with the NUT charge become stronger depends on the Carter constant, the position and velocity of the particles themselves. We also present numerically the changes of the observable velocity and acceleration with the NUT charge for the unbound particles in the Kerr-Taub-NUT spacetime.
We study causal geodesics in the equatorial plane of the extremal Kerr-Taub-NUT spacetime, focusing on the Innermost Stable Circular Orbit (ISCO),and compare its behaviour with extant results for the ISCO in the extremal Kerr spacetime. Calculation of the radii of the direct ISCO, its Kepler frequency, and rotational velocity show that the ISCO coincides with the horizon in the exactly extremal situation. We also study geodesics in the strong {\it non}-extremal limit, i.e., in the limit of vanishing Kerr parameter (i.e., for Taub-NUT and massless Taub-NUT spacetimes as special cases of this sp…
We discuss the tension between the possible existence of Painleve-Gullstrand coordinate systems versus the explicit geometrical features of the Kerr spacetime; a subject of interest to Professor Thanu Padmanabhan in the weeks immediately preceding his unexpected death. We shall carefully distinguish strong and weak Painleve-Gullstrand coordinate systems, and conformal variants thereof, cataloguing what we know can and cannot be done -- sometimes we can make explicit global statements, sometimes we must resort to implicit local statements. For the Kerr spacetime the best that seems to be achiev…
Stability of the rotating string loops in Kerr spacetime
本文研究Kerr时空中赤道面内旋转圆形弦环在赤道与极向扰动下的稳定性，考虑任意状态方程下不同模式的运动，并给出弦环振荡基频的解析表达式。
We analyze the behavior of causal geodesics on a Kerr-de Sitter spacetime with particular emphasis on their completeness property. We set up an initial value problem (IVP) whose solutions lead to a global understanding of causal geodesics on these spacetime. Causal geodesics that avoid the rotation axis are complete except the ones that hit the ring-like curvature singularity and those that encounter the ring singularity are necessary equatorial ones. We also show the existence of geodesics that cross or lie on the rotation axis. The equations governing the latter family show the repulsive nat…
General relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source described by the Kerr gravitational field. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The generalized Jacobi equation for the free motion of a test particle is worked out within the Fermi coordinate system established along the world line of a fiducial observer at rest on the symmetry axis of the exterior Kerr background. The nature of th…
We study properties of a recently proposed new ansatz for separation of variables in the Maxwell equations in four dimensional Kerr-NUT-(A)dS spacetime. We demonstrate that a dual field, which is also a solution of the source-free Maxwell equations, can be presented in a similar form. This result implies that the corresponding separated equations possess a discrete symmetry under a special transform of the separation parameters.
We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.
Regularizing Parameterized Black Hole Spacetimes with Kerr Symmetries
针对参数化 Kerr 时空在无穷远 Taylor 截断后可能产生非物理度规发散的问题，本文通过重定义任意函数消除发散，并提出仅含一至两个任意函数、可精确再现多个已知黑洞解的受限类别，还分析了其 Petrov 类型、振铃频率与阴影形状。
We present a novel solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed. We also study the test body circular equatorial motions in the spacetime.
An asymptotic characterisation of the Kerr spacetime
本文通过共形紧化时空中的渐近特征初值问题，以Killing旋量条件推导自由数据约束，仅用未来零无穷远截面及其与出射零超曲面的交刻画Kerr时空。
We present an integral formulation of observer-dependent Maxwell's equations in curved spacetime and give a classical interpretation of them.
A three-dimensional light-like foliation of a spacetime geometry is one particular way of studying its light cone structure and has important applications in numerical relativity. In this paper, we execute such a foliation for the Kerr-Newman-AdS black hole geometry and compare it with the lightlike foliations of the Kerr-AdS and Kerr-Newman black holes. We derive the equations that govern this slicing and study their properties. In particular, we find that these null hypersurfaces develop caustics inside the inner horizon of the Kerr-Newman-AdS black hole, in strong contrast to the Kerr-AdS c…
We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so characterises this type of data. We first illustrate the characterisation of the Kerr-Newman spacetime in terms of Killing spinors. The space spinor formalism is then used to obtain a set of four independent conditions on an initial Cauchy hypersurface that guarantee the existence of a Killing spinor on the development of the initial data. Following a similar a…
Charged Kerr--Levi-Civita geometries in Einstein--Maxwell and low-energy heterotic string theory
本文构造并比较爱因斯坦-麦克斯韦理论与低能杂化弦理论中带电克尔-列维-奇维塔几何的两种扩展，验证其局域性质，区分局域解生成与全局时空构造。
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 present two complex scalar gauge invariants for perturbations of the Kerr spacetime defined covariantly in terms of the Killing vectors and the conformal Killing-Yano tensor of the background together with the linearized curvature and its first derivatives. These invariants are in particular sensitive to variations of the Kerr parameters. Together with the Teukolsky scalars and the linearized Ricci tensor they form a minimal set that generates all local gauge invariants. We also present curvature invariants that reduce to the gauge invariants in linearized theory.
In this paper we have applied the generalized Kerr-Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike vector fields, from which some properties of the solutions are studied in a coordinate-free way. These spacetimes are algebraically special being their Petrov types II and D. This family includes all the classical vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves, and some other interesting solutions as, for instance, the Kerr m…
In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus the responsible for the Lense-Thirring effect.
Astrometric observations of S-stars provide a unique opportunity to probe the nature of Sagittarius-A* (Sgr-A*). In view of this, it has become important to understand the nature and behavior of timelike bound trajectories of particles around a massive central object. It is known now that whereas the Schwarzschild black hole does not allow the negative precession for the S-stars, the naked singularity spacetimes can admit the positive as well as negative precession for the bound timelike orbits. In this context, we study the perihelion precession of a test particle in the Kerr spacetime geomet…
A speculative model for cyclic information preservation in Kerr-Newman spacetime using closed timelike curves
本文提出一个推测性模型，应用Gavassino恢复原理研究Kerr-Newman黑洞内视界附近闭合类时曲线中粒子的量子信息循环动力学，分析其对量子态演化、纠缠保持和信息留存的影响。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。