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 magnetic fields, from which we obtain nonsingular patterns of an eventual momentum-energy emission of a boosted Kerr-Schild black hole. Distinct patterns are examined and discussed in the case of variations of the boost parameter $γ$. We extend our analysis by considering the nonsingular electromagnetic emission in the framework of a boosted Bondi-Sachs rotating black hole, as it moves at relativistic speeds. We also discuss possible mechanisms that may resemble magnetospheres of rotating boosted black holes and give rise to hydromagnetic flows from accretion discs and to the production of jets.
We discuss a recently presented boosted Kerr black hole solution which had already been used by other authors. This boosted metric is based on wrong assumptions regarding asymptotic inertial observers and moreover the performed boost is not a proper Lorentz transformation. This note aims to clarify some of the issues when boosting black holes and the necessary care in order to interpret them. As it is wrongly claimed that the presented boosted Kerr metric is of Bondi-Sachs type, we recall out some of the necessary requirements and difficulties, when the casting the Kerr metric into a metric wi…
In this paper the spacetime of a general boosted Kerr black hole relative to a Lorentz frame at future null infinity is regarded as a background to examine its respective Papapetrou fields. Taking into account its sole Killing vector we evaluate the electric and magnetic components -- in Bondi-Sachs (BS) and Kerr-Schild (KS) coordinates -- of the Maxwell field which comes from spacetime isometries. To this end we consider a general timelike observer in KS coordinates. Satisfying sufficient conditions for horizon and ergosphere formation it is shown that nonsingular magnetic field configuration…
We obtain the deflection angle for a boosted Kerr black hole in the weak field approximation. We also study the behavior of light in the presence of plasma by considering different distributions: singular isothermal sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We find that the dragging of the inertial system along with the boosted parameter $Λ$ affect the value of the deflection angle. As an application, we studied the magnification for both uniform and SIS distributions.
In this work, we obtain the deflection angle for a boosted Kerr black hole in the weak field approximation using the optics in a curved spacetime developed by J.L. Synge in 1960. We study the behavior of light in the presence of plasma by considering different distributions: uniform plasma, singular isothermal sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We found that the dragging of the inertial system along with the boosted parameter $Λ$ affect the value of the deflection angle. As an application, we studied the magnification for both uniform and singular isoth…
A solution of Einstein's vacuum field equations that describes a boosted Kerr black hole relative to an asymptotic Lorentz frame at the future null infinity is derived. The solution has three parameters (mass, rotation and boost) and corresponds to the most general configuration that an astrophysical black hole must have; it reduces to the Kerr solution when the boost parameter is zero. In this solution the ergosphere is north-south asymmetric, with dominant lobes in the direction opposite to the boost. However the event horizon, the Cauchy horizon and the ring singularity, which are the core …
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.
We investigate gravitational radiation memory and its corresponding effect on the asymptotic symmetries of a body whose exterior is a boosted Schwarzschild spacetime. First, in the context of linearized theory, we consider such a Schwarzschild body which is initially at rest, then goes through a radiative stage and finally emerges as a boosted Schwarzschild body. We show that the proper retarded solution of the exterior Schwarzschild spacetime for this process can be described in terms of the ingoing Kerr-Schild form of the Schwarzschild metric for both the initial and final states. An outgoin…
The Kerr-Schild version of the Schwarzschild metric contains a Minkowski background which provides a definition of a boosted black hole. There are two Kerr-Schild versions corresponding to ingoing or outgoing principle null directions. We show that the two corresponding Minkowski backgrounds and their associated boosts have an unexpected difference. We analyze this difference and discuss the implications in the nonlinear regime for the gravitational memory effect resulting from the ejection of massive particles from an isolated system. We show that the nonlinear effect agrees with the lineariz…
A solution of Einstein's vacuum field equation is derived that describes a general boosted Kerr black hole relative to a Lorentz frame at future null infinity. The metric contains five independent parameters -- mass $m$, rotation $ω$, boost parameter $v/c$ and the boost direction defined by $(n_1,n_2,n_3)$ satisfying $(n_1)^2+(n_2)^2+(n_3)^2=1$ -- and reduces to the Kerr black hole when the boost parameter is zero and $n_1=1$. The solution describes the most general configuration that an astrophysical black hole must have. The black hole rotates about the $z$-axis with angular momentum proport…
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…
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.
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…
Relativistic dynamical friction in Kerr-Schild coordinates
Institut de Ciències del Cosmos (ICC), Universitat de Barcelona（巴塞罗那大学宇宙科学研究所）；Institute for Particle Physics Phenomenology Department of Physics, Durham University（杜伦大学粒子物理现象学系）；School of Mathematical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院数学科学学院）
The exact analytic solutions of the Maxwell equations in the exterior of a boosted rotating black hole immersed in an external magnetic field are obtained. The effect of boost as well as electromagnetic field on charged particle motion and energy extraction process -- magnetic Penrose process around black hole is studied. It justifies however the well known statement that magnetic field greatly increases efficiency of energy extraction which is further boosted by the boost velocity.
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.
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.
Spin-charge induced scalarization of Kerr-Newman black holes in the Einstein-Maxwell-scalar theory with scalar potential
College of Physics and Communication Electronics, Jiangxi Normal University（江西师范大学物理与通信电子学院）；Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）
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.
Superradiance and Quasinormal Modes of Massive Scalar Fields around Kerr Black Holes in Einstein-Maxwell-Dilaton-Axion Theory with Perfect Fluid Dark Matter
Division of Physical Science, Faculty of Science, Prince of Songkla University（宋卡王子大学理学院物理科学系）
The Minkowski background intrinsic to the Kerr-Schild version of the Kerr metric provides a definition of a boosted spinning black hole. There are two Kerr-Schild versions corresponding to ingoing or outgoing principal null directions. The two corresponding Minkowski backgrounds and their associated boosts differ drastically. This has an important implication for the gravitational memory effect. A prior analysis of the transition of a non-spinning Schwarzschild black hole to a boosted state showed that the memory effect in the nonlinear regime agrees with the linearised result based upon the r…
We extend previous work [arXiv:1908.09095] to the case of Maxwell's equations with a source. Our work shows how to construct a retarded vector potential for the Maxwell field on the Kerr-Newman background in a radiation gauge. As in our previous work, the vector potential has a "reconstructed" term obtained from a Hertz potential solving Teukolsky's equation with a source, and a "correction" term which is obtainable by a simple integration along outgoing principal null rays. The singularity structure of our vector potential is discussed in the case of a point particle source.
We consider in this work the asymptotics of a Maxwell field in Schwarzschild and Kerr spacetimes. In any subextremal Kerr spacetime, we show energy and pointwise decay estimates for all components under an assumption of a basic energy and Morawetz estimate for spin $\pm 1$ components. If restricted to slowly rotating Kerr, we utilize the basic energy and Morawetz estimates proven in an earlier work to further improve these decay estimates such that the total power of decay for all components of Maxwell field is $-7/2$. In the end, depending on if the Newman--Penrose constant vanishes or not, w…
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 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.
