Jörg Hennig, Carla Cederbaum, Marcus Ansorg
We prove that in Einstein-Maxwell theory the inequality $(8πJ)^2+(4πQ^2)^2 < A^2$ holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here $J, Q$, and $A$ are angular momentum, electric charge, and horizon area of the black hole, respectively.
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We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum $J$ and charge $Q$ of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation $(8πJ)^2+(4πQ^2)^2=A^+ A^-$, where $A^+$ and $A^-$ denote the areas of event and Cauchy horizon respectively.
We use soliton methods in order to investigate the interior electrovacuum region of axisymmetric and stationary, electrically charged black holes with arbitrary surrounding matter in Einstein-Maxwell theory. These methods can be applied since the Einstein-Maxwell vacuum equations permit the formulation in terms of the integrability condition of an associated linear matrix problem. We find that there always exists a regular inner Cauchy horizon inside the black hole, provided the angular momentum $J$ and charge $Q$ of the black hole do not vanish simultaneously. Moreover, the soliton methods pr…
We present a family of solutions for the axisymmetric Plebanski-Demianski metric and other corresponding reduced metrics. We also present the black hole characteristics using a new set of parameters for Kerr-Newman metric.
We prove the uniqueness theorem for stationary axisymmetric black hole solution in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory. We consider both non-degenerate and extremal Kerr-Sen black hole solutions.
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different features of the fields, such as the derivation of electromagnetic sources for the Maxwell field in the form of thin layers, construction of new solutions, and generation techniques.
We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality $8π|J|<A$ holds, where $J$ is the angular momentum and $A$ the horizon area of the black hole.
We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at the boundary of an electro-vacuum. The Einstein-Maxwell equations in the presence of one Killing vector are obtained by using a projection formalism. The SU(2,1) invariance of the stationary Einstein-Maxwell equations can be used to construct solutions for the electro-vacuum from solutions to the pure vacuum case via a so-called Harrison transformation. It is…
We investigate the interior of regular axisymmetric and stationary black holes surrounded by matter and find that for non-vanishing angular momentum of the black hole the space time can always be extended regularly up to and including an inner Cauchy horizon. We provide an explicit relation for the regular metric at the inner Cauchy horizon in terms of that at the event horizon. As a consequence, we obtain the universal equality $(8πJ)^2 = A^+ A^-$ where $J$ is the black hole's angular momentum and $A^-$ and $A^+$ denote the horizon areas of inner Cauchy and event horizon, respectively. We als…
We studied, both analytically and numerically, an Abelian Higgs vortex in the spacetime of stationary axisymmetric black hole being the solution of the low-energy limit of the heterotic string theory, acted as hair on the black hole background. Taking into account the gravitational backreaction of the vortex we show that its influence is far more subtle than causing only a conical defect. As a consequence of its existence, we found that the ergosphere was shifted as well as event horizon angular velocity was affected by its presence. Numerical simulations reveal the strong dependence of the vo…
We derive inequalities between the area, the angular momentum and the charges for axisymmetric closed outermost stably marginally outer trapped surfaces, embedded in dynamical and, in general, non-axisymmetric spacetimes satisfying the Einstein-Maxwell-dilaton-matter equations. In proving the inequalities we assume that the dilaton potential is nonnegative and that the matter energy-momentum tensor satisfies the dominant energy condition.
Chaotic motion of scalar particle coupling to Chern-Simons invariant in the stationary axisymmetric Einstein-Maxwell dilaton black hole spacetime
本文研究EMDA引力中稳态轴对称黑洞背景下标量粒子与陈-西蒙斯不变量耦合的混沌运动，发现dilation参数、耦合参数和自旋参数共同影响混沌出现的参数范围及混沌强度，表明该耦合导致更丰富的动力学行为。
The properties of a stationary gas cloud surrounding a black hole are discussed, assuming that the gas consists of collisionless, identical massive particles that follow spatially bound geodesic orbits in the Schwarzschild spacetime. Several models for the one-particle distribution function are considered, and the essential formulae that describe the relevant macroscopic observables, like the current density four-vector and the stress-energy-momentum tensor are derived. This is achieved by rewriting these observables as integrals over the constants of motion and by a careful analysis of the ra…
We give a comprehensive discussion, including a detailed proof, of the area-angular momentum-charge inequality for axisymmetric black holes. We analyze the inequality from several viewpoints, in particular including aspects with a theoretical interest well beyond the Einstein-Maxwell theory.
An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of the electromagnetic potential and the metric potential in terms of a solution of the Laplace equation. We give solutions to the Einstein-Maxwell equations with disk sources of finite extension in which the charge density is proportional to the energy surface density. We apply the well-know "inverse" approach to the gravitational potential representing finit…
A lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which satisfy the weak energy condition. If, on the horizon, the given data agree to a certain extent with the associated model Kerr-Newman data, then the inequality reduces to the conjectured Penrose inequality with angular momentum and charge. In addition, a rigidity statement is also proven whereby equality is achieved if and only if the data set arises from the canonical slice of a Kerr-Newman spacetime.
In the present paper we consider 5D spacetimes satisfying the Einstein-Maxwell-dilaton gravity equations which are $U(1)^2$ axisymmetric but otherwise highly dynamical. We derive inequalities between the area, the angular momenta, the electric charge and the magnetic fluxes for any smooth stably outer marginally trapped surface.
We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr-Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.
Using the Harmonic map ansatz, we reduce the axisymmetric, static Einstein-Maxwell equations coupled with a magnetized perfect fluid to a set of Poisson-like equations. We were able to integrate the Poisson equations in terms of an arbitrary function $M=M(ρ,ζ)$ and some integration constants. The thermodynamic equation restricts the solutions to only some state equations, but in some cases when the solution exists, the interior solution can be matched with the corresponding exterior one.
We present an exact solution describing a stationary and axisymmetric object with electromagnetic and dilaton fields. The solution generalizes the usual Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime in general relativity and is obtained by boosting this spacetime in the fifth dimension and performing a Kaluza-Klein reduction to four dimensions. We also discuss the physical parameters of this solution and calculate its gyromagnetic ratio.
Dark photon - dark energy stationary axisymmetric black holes
该研究利用 Ernst 形式体系构造含暗光子与正宇宙学常数的稳态轴对称黑洞解，并在宇宙学常数为零时证明其唯一性定理。
The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell equations. The same transformation can be used to generate a spinning field configuration from any static axisymmetric configuration. We illustrate this by generating from the continuous family of Voorhees--Zipoy vacuum solutions a family of solutions endowed with mass, angular momentum, dipole magnetic moment and quadrupole electric moment.
By using the 't Hooft "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropy arising from the minimally coupled scalar fields which rotate with the azimuthal angular velocity $Ω_0=Ω_H$ ($Ω_H$ is the angular velocity of the black hole horizon) in the general four-dimensional non-extreme stationary axisymmetric black hole space-time. We also show, for the Kerr-Newman and the Einstein-Maxwell dilaton-axion black holes, that the statistical-mechanical entropy obtained from our derivation and the quantum thermodynamical entropy by the conical …
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region a…
Stationary and axisymmetric solutions of relativistic rotating stars with strong mixed poloidal and toroidal magnetic fields are obtained numerically. Because of the mixed components of the magnetic field, the underlying stationary and axisymmetric spacetimes are no longer circular. These configurations are computed from the full set of the Einstein-Maxwell equations, Maxwell's equations and from first integrals and integrability conditions of the magnetohydrodynamic equilibrium equations. After a brief introduction of the formulation of the problem, we present the first results for highly def…
Mass angular momentum and charge inequalities for axisymmetric maximal time-symmetric initial data invariant under an action of U(1) group, in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory, is established. We assume that data set with two asymptotically flat regions is given on smooth simply connected manifold. We also pay attention to the area momentum charge inequalities for a closed orintabler two-dimensional spacelike surface embedded in the spacetime of the considered theory.
We construct exact static, axisymmetric solutions of Einstein-Maxwell-dilaton gravity presenting distorted charged dilaton black holes. The thermodynamics of such distorted black holes is also discussed.
It was originally thought that Bonnor's solution in Einstein-Maxwell theory describes a singular point-like magnetic dipole. Lately, however, it has been demonstrated that indeed it may describe a black {\it dihole}, i.e., a pair of static, oppositely-charged extremal black holes with regular horizons. Motivated particularly by this new interpretation, in the present work, the construction and extensive analysis of a solution in the context of the Brans-Dicke-Maxwell theory representing a black dihole are attempted. It has been known for some time that the solution-generating algorithm of Sing…
Mass formulas are obtained for stationary axisymmetric solutions of the Einstein-Maxwell dilaton-axion theory, which have a regular rod structure on the axis of symmetry. Asymptotic mass, angular momentum and charge are expressed as the sums of masses, angular momenta and charges of rods dressed with field contributions. The calculation is based on a three-dimensional sigma model representation of the stationary EMDA system and the Tomimatsu approach proposed for the Einstein-Maxwell system. Our results provide an alternative interpretation of mass formulas and thermodynamics for black holes w…
We describe stationary and axisymmetric gas configurations surrounding black holes. They consist of a collisionless relativistic kinetic gas of identical massive particles following bound orbits in a Schwarzschild exterior spacetime and are modeled by a one-particle distribution function which is the product of a function of the energy and a function of the orbital inclination associated with the particle's trajectory. The morphology of the resulting configuration is analyzed.
Stable photon orbits in stationary axisymmetric spacetimes with an electromagnetic field and a cosmological constant
本研究将稳定光环的存在性结论推广至含宇宙学常数的时空，证明其可存在于Λ-电真空时空中，却被Λ-真空时空排除，拓展了稳态轴对称时空不稳定性相关研究。
The functional potential formalism is used to analyze stationary axisymmetric spaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendre transformation, a ``Hamiltonian''is obtained, which allows to rewrite the dynamical equations in terms of three complex functions only. Using an ansatz resembling the one used by the harmonic maps ansatz, we express these three functions in terms of the harmonic parameters, studying the cases where these parameters are real, and when they are complex. For each case, the set of equations in terms of these harmonic parameters is derived, and several c…
The first law for stationary axisymmetric multi-black hole systems
研究 Einstein-Maxwell 理论中由 Misner-Dirac 弦连接的旋转带电黑洞共线阵列，推导了涉及面积、角动量和电荷等动力学变量的力学第一定律，并分析了其在电磁对偶性下的不变性。
The magnetic field due to an axially symmetric, hot and highly conducting plasma, taken as an ideal magnetohydrodynamic fluid, surrounding a slow rotating compact gravitational object is studied within the context of Einstein-Maxwell field equations. It is assumed that whereas the plasma is effected by the background spacetime it does not effect the spacetime itself. The Einstein-Maxwell equations are then solved for the magnetic field in a comoving frame with the background spacetime described by the slow rotating Kerr black hole spacetime. It is found that the solutions are magnetic waves tr…
We show that the dilaton Melvin-Schwarzschild black hole is the only asymptotically dilaton Melvin static axisymmetric solution of Einstein-Maxwell dilaton equations of motion.
The properties of an axisymmetric, stationary gas cloud surrounding a massive central object are discussed. It is assumed that the gravitational field is dominated by the central object which is modeled by a nonrelativistic rotationally-symmetric potential. Further, we assume that the gas consists of collisionless, identical massive particles that follow bound orbits in this potential. Several models for the one-particle distribution function are considered and the essential formulae that describe the relevant macroscopical observables, such as the particle and energy densities, pressure tenso…
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。
Gauge-Theoretical Method in Solving Zero-curvature Equations II--Non-Weyl Class Solutions of the Static Einstein-Maxwell Equations
本文通过规范理论方法求解静态爱因斯坦-麦克斯韦方程，得到非韦伊类解，并在静电和磁静情况下分别给出了与邦纳解一致及描述两个磁荷质量引力场的解。
A simple proof of a strengthened form of the first law of black hole mechanics is presented. The proof is based directly upon the Hamiltonian formulation of general relativity, and it shows that the the first law variational formula holds for arbitrary nonsingular, asymptotically flat perturbations of a stationary, axisymmetric black hole, not merely for perturbations to other stationary, axisymmetric black holes. As an application of this strengthened form of the first law, we prove that there cannot exist Einstein-Maxwell black holes whose ergoregion is disjoint from the horizon. This closes…
Angular momentum and mass-charge inequalities for axisymmetric maximal time-symmetric initial data in Einstein-Maxwell gravity with dark matter sector were derived. The dark matter sector is mimicked by another U(1)-gauge field coupled to the ordinary Maxwell one. We assume that data set with two asymptotically flat regions is given on smooth simply connected manifold. One also pays attention to the area momentum charge inequalities for a closed orientable two-dimensional spacelike surface embedded in the spacetime of the considered theory. It turned out that the addition of dark matter sector…
Uniqueness of stationary axisymmetric type D black holes with non-aligned electromagnetic field
本文证明了轴对称类型D时空的唯一性，展示了在爱因斯坦-麦克斯韦理论中，非对齐电磁场的唯一非平凡电真空解是Ovcharenko-Podolsky类。
Choked accretion onto Kerr-Sen black holes in Einstein-Maxwell-dilaton-axion gravity
本文研究爱因斯坦-麦克斯韦-膨胀子-轴子引力中克尔-森黑洞的超相对论流体吸积过程，发现膨胀子参数增大时喷射率与注入率之比增大，辐射效率更高而红移更低。
The extended scalar-tensor and vector-tensor theories admit black hole solutions with the nontrivial profiles of the scalar and vector fields, respectively. The disformal transformation maps a solution in a class of the scalar-tensor or vector-tensor theories to that in another class, and hence it can be a useful tool to construct a new nontrivial solution from the known one. First, we investigate how the stationary and axisymmetric solutions in the vector-tensor theories without and with the $U(1)$ gauge symmetry are disformally transformed. We start from a stationary and axisymmetric solutio…
Three non-existence results are established for self-gravitating solitons in Einstein-Maxwell-scalar models, wherein the scalar field is, generically, non-minimally coupled to the Maxwell field via a scalar function $f(Φ)$. Firstly, a trivial Maxwell field is considered, which yields a consistent truncation of the full model. In this case, using a scaling (Derrick-type) argument, it is established that no stationary and axisymmetric self-gravitating scalar solitons exist, unless the scalar potential energy is somewhere negative in spacetime. This generalises previous results for the static and…
We show that non-degenerate multiple black hole solution of Einstein- Maxwell equations in an asymptotically flat axisymmetric spacetime cannot be in stationary equilibrium. This extends the uniqueness of Kerr-Newman solution first proved by Bunting and Mazur in a much wider desirable class. Spin-spin interaction cannot hold the black hole aparts even with electromagnetic forces.
Polarized Image of a Synchrotron-emitting Ring in Einstein-Maxwell-scalar Theory
该研究模拟Einstein-Maxwell-scalar理论中带毛黑洞周围同步辐射环的偏振图像，发现非最小耦合会增强偏振强度并改变电矢量位置角，从而为观测区分带毛黑洞与Schwarzschild黑洞提供线索。
Radiation properties of the accretion disk around a black hole in Einstein-Maxwell-scalar theory
本研究探讨了EMS理论中非旋转黑洞的性质，确定了其吸积盘粒子的轨道参数及ISCO，并分析了不同黑洞参数下的辐射效率、通量、微分光度与温度。
A master equation for Carter-separable stationary axisymmetric spacetimes and compatible sources
本文证明稳态轴对称时空中Carter投影扇区的剩余对角爱因斯坦方程等价于一个带源的主方程，并恢复真空-Λ Kerr-Carter和Plebański-Demiański族作为解。
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes. We also weaken the hypotheses used in the proof of this result for single black holes, and establish the associated rigidity statement.
One-sided type-D metrics with aligned Einstein-Maxwell
研究四维Riemannian度规下type-D Weyl张量与Maxwell场对齐的Einstein-Maxwell方程，证明其可由$SU(\infty)$-Toda场方程或三维Laplacian的轴对称解表示，从而实现场方程线性化。
The rotating solutions beyond the spontaneous scalarization in Einstein-Maxwell-scalar theory
该研究用谱方法数值求解四次耦合EMS理论中的旋转标量化黑洞，确定其自旋-电荷存在域，并揭示自旋对两支解热力学差异及标量场赤道集中分布的影响。
Rotating black hole solutions for $f(R)$ gravity and Newman Janis Algorithm
该研究证明常Ricci标量的$f(R)$引力可由带宇宙学项和修正引力常数的Einstein类引力描述，提出改进的Newman-Janis算法求其旋转轴对称解，并借助对偶性说明Einstein类引力的静/稳态解也是对应$f(R)$引力的解。
FPIC: a new Particle-In-Cell code for stationary and axisymmetric black-hole spacetimes
本文介绍新开发的GRPIC代码FPIC，采用球形Kerr-Schild坐标和混合粒子推进器，在降低计算成本的同时改善能量守恒，并成功模拟Wald解和Blandford-Znajek光度。
Black holes in rotating, electromagnetic backgrounds and topological Kerr-Newman-NUT spacetimes
本文研究了旋转电磁背景中黑洞解的分类，发现所有已知的轴对称且规则背景均属于拓扑Kerr-Newman-NUT度规的双威克旋转家族，提出了Schwarzschild黑洞嵌入新背景的解。
We analyze the relativistic dynamical properties of Keplerian and non-Keplerian circular orbits in a general axisymmetric and stationary gravitational field, and discuss the implications for the stability of co- and counter-rotating accretion disks and tori surrounding a spinning black hole. Close to the horizon there are orbital peculiarities which can seem counterintuitive, but are elucidated by formulating the dynamics in terms of the orbital velocity actually measured by a local, zero-angular-momentum observer.
Charged black holes surrounded by shells of charged particles
本文构造了Einstein-Vlasov-Maxwell系统的新静态解，用于模拟被带电物质壳层包围的Reissner-Nordstrom型黑洞。
After considering the quantum corrections of Einstein-Maxwell theory, the effective theory will contain some higher-curvature terms and nonminimally coupled electromagnetic fields. In this paper, we study the first law of black holes in the gravitational electromagnetic system with the Lagrangian $\math{L}(g_{ab}, R_{abcd}, F_{ab})$. Firstly, we calculate the Noether charge and the variational identity in this theory, and then generically derive the first law of thermodynamics for an asymptotically flat stationary axisymmetrical symmetric black hole without the requirement that the electromagn…
Thin accretion disk around black hole in Einstein-Maxwell-scalar theory
本文在爱因斯坦-麦克斯韦-标量引力框架下研究超大质量黑洞薄吸积盘，揭示了参数α和β对辐射通量、温度、光度及辐射效率的不同影响，为黑洞天文观测提供理论参考。
We present a generalization of the black hole solution with spherical symmetry already known in the literature for $N$-dimensional $F(R)$ gravity with a conformally invariant Maxwell field and constant scalar curvature $R$. This solution also includes a generalization of the one corresponding to general relativity as a special case. We introduce the formalism for the construction of a broad family of spherically symmetric thin shells in $F(R)$ theory. We use our generalized solution in order to provide examples of bubbles and thin layers of matter surrounding black holes. We analyze the stabil…
This work establishes critical phenomena in the topological transition of black hole coalescence. We describe and validate a computational front tracking event horizon solver, developed for generic studies of the black hole coalescence problem. We then apply this to the Kastor - Traschen axisymmetric analytic solution of the extremal Maxwell - Einstein black hole merger with cosmological constant. The surprising result of this computational analysis is a power law scaling of the minimal throat proportional to time. The minimal throat connecting the two holes obeys this power law during a short…
We present new solutions to the Einstein-Maxwell equations representing a class of charged distorted black holes. These solutions are static-axisymmetric and are generalizations of the distorted black hole solutions studied by Geroch and Hartle. Physically, they represent a charged black hole distorted by external matter fields. We discuss the zeroth and first law for these black holes. The first law is proved in two different forms, one motivated by the isolated horizon framework and the other using normalizations at infinity.
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