The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas $et~al.$ put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole. We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter. We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter. The resulting formula for the energy extraction improves the agreement with numerical simulations at finite spin. Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well. Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.
The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined,…
The Blandford-Znajek mechanism is the continuous extraction of energy from a rotating black hole via plasma currents flowing on magnetic field lines threading the horizon. In the discovery paper, Blandford and Znajek demonstrated the mechanism by solving the equations of force-free electrodynamics in a perturbative expansion valid at small black hole spin. Attempts to extend this perturbation analysis to higher order have encountered inconsistencies.We overcome this problem using the method of matched asymptotic expansions, taking care to resolve all of the singular surfaces (light surfaces) i…
From a spacetime perspective, the dynamics of magnetic field lines of force-free electromagnetic fields can be rewritten into a quite similar form for the dynamics of strings, i.e., dynamics of "field sheets". Using this formalism, we explicitly show that the field sheets of stationary and axisymmetric force-free electromagnetic fields have identical intrinsic properties to the world sheets of rigidly rotating Nambu-Goto strings. Thus, we conclude that the Blandford-Znajek process is kinematically identical to an energy-extraction mechanism by the Nambu-Goto string with an effective magnetic t…
We consider the Blandford-Znajek process of electromagnetic extraction of energy from a general axially symmetric asymptotically flat slowly rotating black hole. Using the general parametrization of the black-hole spacetime we construct formulas for the flux of the magnetic field and the rate of energy extraction, which are valid not only for the Kerr spacetime, but also for its arbitrary axially symmetric deformations. We show that in the dominant order these quantities depend only on a single deformation parameter, which relates the spin frequency of a black hole with its rotation parameter.
We study the metric backreaction of mass and angular momentum accretion on black holes. We first develop the formalism of monopole and dipole linear gravitational perturbations around the Schwarzschild black holes in the Eddington-Finkelstein coordinates against the generic time-dependent matters. We derive the relation between the time dependence of the mass and angular momentum of the black hole and the energy-momentum tensors of accreting matters. As a concrete example, we apply our formalism to the Blandford-Znajek process around the slowly rotating black holes. We find that the time depen…
According to the Blandford-Znajek mechanism, black hole jets are powered by the rotational energy of the compact object. In this work, we consider the possibility that the metric around black holes may not be described by the Kerr solution and we study how this changes the Blandford-Znajek model. If the Blandford-Znajek mechanism is responsible for the formation of jets, the estimate of the jet power in combination with another measurement can test the nature of black hole candidates and constrain possible deviations from the Kerr solution. However, this approach might become competitive with …
The Blandford-Znajek mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In such mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In the current work we examine the behaviour of the BZ mechanism with respect to different boundary conditions, revealing the mechanism robustness upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.
The Blandford-Znajek process, the steady electromagnetic energy extraction from a rotating black hole, is widely believed to work for driving relativistic jets, although it is still under debate where the electric current is driven. We address this issue analytically by investigating the time-dependent state in the Boyer-Lindquist and Kerr-Schild coordinate systems. This analysis suggests that a non-ideal magnetohydrodynamic region is required in the time-dependent state, while not in the steady state.
Blandford and Znajek discovered a process by which a spinning black hole can transfer rotational energy to a plasma, offering a mechanism for energy and jet emissions from quasars. Here we describe a version of this mechanism that operates with only vacuum electromagnetic fields outside the black hole. The setting, which is not astrophysically realistic, involves either a cylindrical black hole or one that lives in 2+1 spacetime dimensions, and the field is given in simple, closed form for a wide class of metrics. For asymptotically Anti-de Sitter black holes in 2+1 dimensions the holographic …
The Blandford-Znajek theory (1977) is generally studied to understand the generation of powerful relativistic jets. However, it could also give important insights about the feedback between a rotating black hole, its ergosphere, and a surrounding accretion disk. The energy flow between these systems could be understood by studying the BZ power as a function of a slip factor, which in turn is defined as a function of the angular velocity of the black hole and the angular velocity of the magnetic field lines (generally anchored to the disk). The distinct stages could explain the different types …
Spinning black holes tend to expel magnetic fields. In this way they are similar to superconductors. It has been a persistent concern that this black hole "Meissner effect" could quench jet power at high spins. This would make it impossible for the rapidly rotating black holes in Cyg X-1 and GRS 1915+105 to drive Blandford-Znajek jets. We give a simple geometrical argument why fields which become entirely radial near the horizon are not expelled by the Meissner effect and may continue to power jets up to the extremal limit. A simple and natural example is a split-monopole field. We stress that…
The superradiant scattering of Alfvén waves (Alfvénic superradiance) in a forcefree magnetosphere is discussed to reveal the relationship between the Blandford-Znajek (BZ) process and superradiance. For simplicity, we consider a four-dimensional rotating black string spacetime of which each $z=\text{const}$ slice is a Bañados-Teitelboim-Zanelli solution as an analogy of the equatorial plane of the Kerr spacetime. Then, it is confirmed that the condition for Alfvénic superradiance coincides with that for the BZ process, and the wave amplification can be very large due to a resonant scattering f…
The Blandford-Znajek (BZ) mechanism describes a physical process for the energy extraction from a spinning black hole (BH), which is believed to power a great variety of astrophysical sources, such as active galactic nuclei (AGNs) and Gamma ray bursts (GRBs). The only known analytic solution to the BZ mechanism is a split monopole perturbation solution up to $O(a^2)$, where $a$ is the spin parameter of a Kerr black hole. In this paper, we extend the monopole solution to higher order $\sim O(a^4)$. We carefully investigate the structure of the BH magnetosphere, including the angular velocity of…
The Blandford-Znajek process, one of the most promising model for powering the relativistic jets from black holes, was initially introduced as a mechanism in which the magnetic fields extract energy from a rotating black hole. We study the evolution of force-free electromagnetic fields on regular spacetimes with an ergosphere, which are generated by rapidly rotating stars. Our conclusive results confirm previous works, claiming that the Blandford-Znajek mechanism is not directly related to the horizon of the black hole. We also show that the radiated energy depends exponentially on the compact…
The Blandford-Znajek process, which uses a magnetized plasma to extract energy from a rotating black hole, is one of the leading candidates for powering relativistic jets. In this work, we investigate the Blandford-Znajek process in two well-motivated quadratic gravity theories: scalar Gauss-Bonnet and dynamical Chern-Simons gravity. We solve analytically for a split-monopole magnetosphere to first order in the small-coupling approximation and second relative order in the slow-rotation approximation. The extracted power at fixed spin and magnetic flux is enhanced in scalar Gauss-Bonnet and red…
We analyze the constraint equation giving allowed solutions describing fields and currents in a force-free magnetosphere around a rotating black hole. Utilizing the divergence properties of the energy and angular-momentum fluxes for physically allowed solutions, we conclude that poloidal surfaces are independent of the radial coordinate for large values of $r$. Using this fact and the Znajek regularity condition, we explicitly derive all possible exact solutions admitted by the constraint equation for $r$ independent poloidal surfaces, which are given in terms of the electromagnetic angular ve…
One of the mechanisms widely considered for driving relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts is the electromagnetic extraction of the rotational energy of a central black hole, i.e., the Blandford-Znajek process, although the origin of the electromotive force in this process is still under debate. We study this process as the steady unipolar induction in the Kerr black hole magnetosphere filled with a collisionless plasma screening the electric field (the D field) along the magnetic field (the B field), i.e., D dot B = 0. We extend the formulatio…
Blandford-Znajek process, the steady electromagnetic energy extraction from a rotating black hole (BH), is widely believed to work for driving relativistic jets in active galactic nuclei, gamma-ray bursts and Galactic microquasars, although it is still under debate how the Poynting flux is causally produced and how the rotational energy of the BH is reduced. We generically discuss the Kerr BH magnetosphere filled with a collisionless plasma screening the electric field along the magnetic field, extending the arguments of Komissarov and our previous paper, and propose a new picture for resolvin…
Blandford-Znajek (BZ) mechanism has usually been studied in the literature for accretion with considerably high angular momentum leading either to the formation of a cold Keplerian disc, or a hot and geometrically thick sub-Keplerian flow as described within the framework of ADAF/RIAF. However, in nearby elliptical galaxies, as well as for our own Galactic centre, accretion with very low angular momentum is prevalent. Such quasi-spherical strongly sub-Keplerian accretion has complex dynamical features and can accommodate stationary shocks. In this letter, we present our calculation for the max…
A toy model for the Blandford-Znajek mechanism is investigated: a Kerr black hole with a toroidal electric current residing in a thin disk around the black hole. The toroidal electric current generates a poloidal magnetic field threading the black hole and disk. Due to the interaction of the magnetic field with remote charged particles, the rotation of the black hole and disk induces an electromotive force, which can power an astrophysical load at remote distance. The power of the black hole and disk is calculated. It is found that, for a wide range of parameters specifying the rotation of the…
Recent general relativistic MHD simulations have suggested that relativistic jets from active galactic nuclei (AGNs) have been powered by rotational energy of central black holes. Some mechanisms of extraction of black hole rotational energy have been proposed, like the Penrose process, Blandford-Znajek mechanism, MHD Penrose process, and superradiance. The Blandford-Znajek mechanism is the most promising mechanism for the engines of the relativistic jets from AGNs. However, an intuitive interpretation of this mechanism with causality is not clarified yet, while the Penrose process has a clear…
As a complementary or companion process to the Blandford-Znajek mechanism for the rotational energy extraction from a Kerr black hole to serve as a viable model for the central engine of quasar, AGN and even GRB, the magnetic alignment process is proposed. In contrast to the environment assumed in the Blandford-Znajek mechanism in which the rotating hole's spin axis and the asymptotic direction of the magnetic field are aligned, this new process operates when they are generally misaligned which obviously is the more natural situation likely to happen. The time scales over which these two proce…
The Blandford-Znajek constraint equation for a stationary, axisymmetric black-hole force-free magnetosphere is cast in a 3+1 absolute space and time formulation, following Komissarov (2004). We derive an analytic solution for fields and currents to the constraint equation in the far-field limit that satisfies the Znajek condition at the event horizon. This solution generalizes the Blandford-Znajek monopole solution for a slowly rotating black hole to black holes with arbitrary angular momentum. Energy and angular momentum extraction through this solution occurs mostly along the equatorial plan…
Blandford-Znajek Scaling in a Power-Law Rotating Kalb-Ramond Geometry: Magnetic-Flux Systematics and Bayesian Identifiability
New Uzbekistan University（新乌兹别克斯坦大学）；Tashkent State Technical University（塔什干国立技术大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Kimyo International University in Tashkent（塔什干化学国际大学）；Samarkand State Technical University named after Mirzo Ulugbek（米尔佐·乌鲁伯格撒马尔罕国立技术大学）；Samarqand State Pedagogical Institute（撒马尔罕国立师范学院）
Numerical simulations of Blandford-Znajek energy extraction at high spin have revealed that field lines tend to bunch near the poles of the event horizon. We show that this behavior can be derived analytically from the assumption of fixed functional dependence of current and field line rotation on magnetic flux. The argument relies crucially on the existence of the Znajek condition, which offers non-trivial information about the fields on the horizon without requiring a full force-free solution. We also provide some new analytic expressions for the parabolic field configuration.
In this lecture I give an introduction to the rotational energy extraction of black holes by the electromagnetic Blandford-Znajek process and the generation of relativistic jets. After some basic material on the electrodynamics of black hole magnetospheres, we derive the most important results of Blandford and Znajek by making use of Kerr-Schild coordinates, which are regular on the horizon. In a final part we briefly describe results of recent numerical simulations of accretion flows on rotating black holes, the resulting large-scale outflows, and the formation of collimated relativistic jets…
In the Penrose process and the Blandford-Znajek mechanism, the rotational energy of a black hole (BH) is extracted via particle fission and magnetic tension, respectively. Recently, inspired by a fundamental trait in plasma astrophysics known as magnetic reconnection (MR), a new energy extraction mechanism based on the fast reconnection of the magnetic field lines inside the ergosphere has been proposed by Comisso and Asenjo. In this paper, we investigate energy extraction caused by MR in the ergosphere of a rapidly spinning BH with broken Lorentz symmetry by a background bumblebee vector fiel…
The structural properties of geodesic currents in an ambient Kerr background is studied from an analytical point of view. The geodesics in the congruence correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes.
We present analytic force-free solutions modeling rotating stars and black holes immersed in the magnetic field of a thin disk that terminates at an inner radius. The solutions are exact in flat spacetime and approximate in Kerr spacetime. The compact object produces a conical jet whose properties carry information about its nature. For example, the jet from a star is surrounded by a current sheet, while that of a black hole is smooth. We compute an effective resistance in each case and compare to the canonical values used in circuit models of energy extraction. These solutions illustrate all …
Recent work has called into question whether nature can extract the rotational energy of a black hole via electromagnetic fields by appealing to an alleged ability to absorb current. We describe the strategies needed to properly treat the astrophysics in curved spacetime near black holes, showing that while the Blandford-Znajek effect is sound, the deeper nature of the electric nature of black holes remains unresolved.
Black holes can accumulate a large amount of energy, responsible for highly energetic astrophysical phenomena Recently, fast magnetic reconnection (MR) of the magnetic field was proposed as a new way to extract energy and in this paper, we investigate this phenomena in a bumblebee Kerr-Sen BH. We find that the presence of the charge parameter strongly changes the simple Kerr case, making this extraction mechanism possible even for not extremely rotating black holes ($a \sim 0.7$). We also show that, under appropriate circumstances, MR is more efficient compared to the Blandford-Znajek mechanis…
Energy extraction from a rotating Buchdahl star via magnetic reconnection
New Uzbekistan University（新乌兹别克斯坦大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究大学TIIAME基础与应用研究所）；Tashkent University of Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
We study scalar field configurations around Kerr black holes with a time-independent energy-momentum tensor. These stationary `scalar clouds', confined near the black hole (BH) by their own mass or a mirror at fixed radius, exist at the threshold for energy extraction via superradiance. Motivated by the electromagnetic Blandford-Znajek (BZ) mechanism, we explore whether scalar clouds could serve as a proxy for the force-free magnetosphere in the BZ process. We find that a stationary energy-extracting scalar cloud solution exists when the reflecting mirror is replaced by a semi-permeable surfac…
We calculate the evolution of the prompt intrinsic Poynting power generated by merging black holes. Orbiting black holes induce rotation of the space-time. In a presence of magnetic field supported by an accretion disk outside of the orbit, this results in a generation of an electromagnetic outflow via the Blandford-Znajek-type process with luminosity $L_{EM} \sim G^3 M^3 B^2/(c^5 R_{orb}) $ and reaching a fairly low maximum values of $L_{EM} = 10^{37}-10^{39} m_6 $ erg s$^{-1}$ ($m_6$ is the masses of black holes in millions of Solar mass) at the time of the merger. Dissipation of the wind po…
Blandford-Znajek (BZ) mechanism describes a process extracting rotation energy from a spinning black hole (BH) via magnetic field lines penetrating the event horizon of central BH. In this paper, we present a perturbation approach to study force-free jets launched by the BZ mechanism, and its two immediate applications: (1) we present a high-order split monopole perturbation solution to the BZ mechanism, which accurately pins down the energy extraction rate $\dot E$ and well describes the structure of BH magnetosphere for all range of BH spins ($0\leq a\leq 1$); (2) the approach yields an exac…
The extraction of rotational energy from a spinning black hole via the Blandford-Znajek mechanism has long been understood as an important component in models to explain energetic jets from compact astrophysical sources. Here we show more generally that the kinetic energy of the black hole, both rotational and translational, can be tapped, thereby producing even more luminous jets powered by the interaction of the black hole with its surrounding plasma. We study the resulting Poynting jet that arises from single boosted black holes and binary black hole systems. In the latter case, we find tha…
We discuss stationary and axisymmetric trans-magnetosonic outflows in the magnetosphere of a rotating black hole (BH). Ejected plasma from the plasma source located near the BH is accelerated far away to form a relativistic jet. In this study, the plasma acceleration efficiency and conversion of fluid energy from electromagnetic energy are considered by employing the trans-fast magnetosonic flow solution derived by Takahashi & Tomimatsu (2008). Considering the parameter dependence of magnetohydrodynamical flows, we search for the parameters of the trans-magnetosonic outflow solution to the rec…
Energy extraction from a Kerr-Bardeen-Letelier black hole by Comisso-Asenjo Mechanism
IUCAA, Pune, Maharashtra（印度大学天体物理与宇宙学中心）；School of Physics, Damghan University, Iran（达姆甘大学物理学院）；Department of Physics, Banaras Hindu University, Varanasi - 221005, Uttar Pradesh, India（贝拿勒斯印度教大学）；Department of Physics, Institute of Applied Sciences and Humanities, GLA University, Mathura - 281406, Uttar Pradesh, India（GLA大学应用科学与人文学院）
