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We discuss the feature of the magnetic field configuration arising from double counter oriented electric current-rings in the accretion disc around a Kerr black hole (BH). We discuss the relevant physical quantities corresponding to this configuration: (1) the power and torque transferred by the large-scale magnetic field, (2) the angular momentum and energy fluxes transferred from the BH to the inner disc, (3) the radiation flux from the disc. In addition, we discuss the possibility that the closed magnetic field anchored at the disc probably evolves to the open magnetic field, which is helpful to produce the jet from the disc.

An analytical expression for the jet power extracted from the plunging region between a black hole (BH) horizon and the inner edge of the disk (hereafter the PL power) is derived based on an improved equivalent circuit in BH magnetosphere with a mapping relation between the radial coordinate of the plunging region and that of the remote astrophysical load. It is shown that the PL power is of great importance in explaining jet power and dominates over the BZ and DL powers for a wide value range of the BH spin. In addition, we show that the PL power derived in our model can be fitted with the strong jet powers of several 3CR FR I radio galaxies, which cannot be explained by virtue of the BZ mechanism. Furthermore, the condition for negative energy of the accreting particles in the plunging region is discussed with the validity of the second law of BH thermodynamics.

Correlations of active galactic nuclei (AGNs) with microquasars are discussed based on the coexistence of the Blandford–Znajek (BZ) and magnetic coupling (MC) processes (CEBZMC) in black hole (BH) accretion disk. The proportions of several quantities of BH systems for both AGNs and microquasars are derived by combining the observational data with CEBZMC. It is shown that the square of the magnetic field at the BH horizon is inversely proportional to the BH mass, while the accretion rate of the disk is proportional to the BH mass. In addition, the very steep emissivity indexes from the recent XMM-Newton observations of the nearby bright Seyfert 1 galaxy MCG-6-30-15 and the microquasars XTE J1650-500 are well fitted by considering the MC effects on the disk radiation. These results suggest strongly the correlations of AGNs with microquasars.

Based on the coexistence of the Blandford–Znajek and magnetic coupling processes in black hole (BH) accretion disc, a multi-parameter model for jet powers and radio loudness of active galactic nuclei (AGNs) is studied. It turns out that radio-loudness of AGNs could be governed by five parameters: (i) the BH spin, (ii) a power-law index of the variation of the magnetic field on the disc; (iii) a parameter determining the position of the inner edge of the disc, (iv) the ratio of the pressure of the magnetic field on the horizon to the ram pressure of the innermost parts of an accretion flow, and (v) the ratio of the angular velocity of the open field lines to that of the horizon. The observed dichotomy between radio-loud and radio-quiet AGNs is well interpreted by the effects of the above parameters. Furthermore, we discuss the derivative of radio loudness of AGNs with respect to each parameter separately. In addition, the effect of the screw instability on radio loudness of AGNs is discussed.

A new approach of detecting the black hole spin in x-ray binaries is proposed based on the model of the coexistence of the Blandford–Znajek (BZ) and magnetic coupling (MC) processes, in which the BZ process is used to power the jet emissions from x-ray binaries, and high frequency quasi-periodic oscillations (QPOs) are explained by a rotating hotspot in the inner region of the accretion disc surrounding a fast-spinning black hole. It is shown that the black hole spins of several x-ray binaries (XTE J1550-564, GRO J1665-40 and GRS 1915+105) can be constrained in a rather narrow range, provided that QPOs and jets coexist in these sources.

The screw instability of the magnetic field is discussed based on its poloidal configuration generated by a single toroidal electric current flowing in the equatorial plane of a Kerr black hole (BH). The rotation of the BH relative to the disc induces an electromotive force, which in turn results in a poloidal electric current. By using Ampere's law, we calculate the toroidal component of the magnetic field and derive a criterion for the screw instability of the magnetic field connecting the rotating BH with its surrounding disc. It is determined that the screw instability is related to two parameters: the radius of the disc and the BH spin. The occurrence of screw instability is depicted in a parameter space. In addition, we discuss the effect of the screw instability on magnetic extraction of energy from the rotating BH.

Magnetic extraction of energy from a rotating black hole (BH) is discussed in the coexistence of the Blandford–Znajek (BZ) process and the magnetic coupling (MC) process by considering the effects of the screw instability of the magnetic field. It is shown that the screw instability affects the configuration of the magnetosphere and the evolution characteristics of the BH, augmenting the energy extracted in the BZ and MC processes. In addition, the observed energy and duration of several gamma-ray bursts can be fitted well by virtue of our model.

A new configuration of magnetic field (NCMF) in black hole (BH) magnetosphere is proposed by considering the effects of the screw instability. Three mechanisms of extracting energy magnetically are involved in the NCMF: (1) the Blandford–Znajek (BZ) process; (2) the magnetic coupling (MC) process; (3) a new scenario (henceforth the DL process) for extracting rotational energy from the disc, which is related to the open field lines connecting the disc with the astrophysical load. The expressions for the powers and torques of the above energy mechanisms are derived by using two kinds of the equivalent circuits. It turns out that the power and efficiency of extracting energy magnetically from the BH accretion disc are all augmented in the NCMF. It is shown that a very steep emissivity can be produced in a NCMF, which is consistent with the recent XMM-Newton observation of the nearby bright Seyfert 1 galaxy MCG-6-30-15.

The profiles of emission lines and images of an accretion disc around a black hole (BH) are simulated by considering the effects of the magnetic coupling (MC) of a central BH with the disc. The MC effects are discussed for both slow- and fast-spinning BHs, and the following results are obtained. Firstly, the width of the emission lines and the brightness of the disc are reduced and augmented for slow- and fast-spinning BHs, respectively. Secondly, the image of the disc becomes dimmer and brighter near the inner edge of the disc for slow- and fast-spinning BHs, respectively. It turns out that all these results arise from the MC effects on the position of the dominant emission region of the accretion disc.

An analytical expression for the jet power extracted from the disc (JPEFD) is derived based on an equivalent circuit in black hole magnetosphere with a mapping relation between the radial coordinate of the disc and that of unknown astrophysical load. It turns out that this JPEFD is comparable with two other JPEFDs derived in the Poynting flux and hydrodynamic regimes, respectively. In addition, the relative importance of this JPEFD relative to the Blandford–Znajek power is discussed. It is shown that the BZ power is generally dominated by the JPEFD except in some extreme cases. Furthermore, we show that the JPEFD derived in our model can be well fitted with the jet power of 3C 273.

The correlation of screw-instability in black hole magnetosphere with pairs of high-frequency quasi-periodic oscillations (HFQPOs) is discussed in the coexistence of the Blandford–Znajek (BZ) and magnetic coupling (MC) processes. It turns out that screw-instability can result in HFQPOs. Such an HFQPO can be regarded as the transient process in an equivalent circuit with resistor and inductor in series (R-L circuit), and its period can be estimated by the relaxation time of this process. When the BZ process and the MC process coexist, the screw-instability can occur both in the BZ region and in the MC region, and the pairs of HFQPOs can be generated. Calculations show that such pairs of HFQPOs are likely to show frequencies in a 3:2 ratio. The frequencies of pairs of HFQPOs in our model scale inversely with the mass of central black hole, which is consistent with the observations.

Screw instability of the magnetic field connecting a rotating black hole (BH) with its surrounding disc is discussed in coexistence with the Blandford–Znajek (BZ) process and the magnetic coupling (MC) process. A scenario for kilohertz quasi-periodic oscillations (kHz QPOs) in x-ray binaries is proposed by introducing inductance components in the equivalent circuit for BH magnetosphere. It turns out that the period related to the screw instability is consistent with the observations of kHz QPO x-ray binaries.

The cycle of black hole (BH) spin proposed by Li and Paczynski (henceforth CYCLP) is compared with a more natural model (henceforth CYC03), in which energy and angular momentum are transferred from a rotating BH to a region of some widths by the closed magnetic field lines. It turns out that the efficiency of converting the accreted mass into the radiation energy in the CYC03 is less than that estimated in the CYCLP, while the BH mass and entropy in the CYC03 are greater than those in the CYCLP. It is shown that the features of the CYC03 are insensitive to the power-law index indicating the variation of the magnetic field in the disc.

Evolution characteristics of a rotating black hole (BH) are discussed in coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process in the parameter space consisting of the BH spin and the power-law index of the magnetic field on the disc. The condition for the coexistence of the two energy mechanisms are derived by using the mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the disc. It is shown that not only the two mechanisms can coexist, but also the power and the rate of change of BH entropy in the BZ process will dominate over those in the MC process, provided that the BH spin and the power-law index are great enough.

A toy disc model with advection dominated accretion on to a black hole is presented. The advection dominated accretion flows (ADAFs) are assumed to exist in the inner thick disc with rin rout. Compared with Paczynski's toy model the thick disc is not limited to be 100% advective. It turns out that the inner radius rin depends not only on the outer radius rout but also on the ADAF parameters f and e. The effects of the inner thick disc on the radiation efficiency and the temperature profile of the outer thin disc are discussed in details.

An analytical model of black hole (BH) evolution is proposed by considering the Blandford-Znajek process with a transient magnetized accretion disc, which is used as a central engine for powering gamma ray bursts (GRBs). The state of BH evolution can be described by the representative points in the corresponding sub-regions of a parameter space. It is shown that the BH spin might be spun up rather than slowed down, provided that the ratio of the angular velocity of the magnetic field lines to that of the BH horizon is greater than a critical value. In addition, the effects of some initial values of the BH system on the evolution terminals and the output energy for GRBs are discussed in the parameter space.

Two new mapping relations between the angular coordinate on the black hole (BH) horizon and radial coordinate on the disc are given according to the requirement of general relativity and Maxwell's equations, and the effects of magnetic coupling (MC) on temperature of accretion disc are investigated by comparing with pure accretion. It is shown that the MC effects on the temperature profile are related intimately to the BH spin, and the influence on the peak value of disc temperature based on the modified mapping relations is not as great as that based on the linear mapping. The peak value and the corresponding radius of peak value ring of disc temperature do not increase monotonically as the increasing spin of BH, each containing a maximum for the fast-spinning BH. The value ranges of the bolometric luminosity and color temperature of the disc are both extended by the MC effects.

We propose a model of the magnetic coupling (MC) of a rotating black hole (BH) with the surrounding accretion disc in order to study the radial temperature profile in the inner region of the disc, in which a linear map from the angular coordinate on the BH horizon to the radial coordinate on the thin disc is given by closed magnetic field lines. The MC power and torque are derived using a modified equivalent circuit. It is shown that the MC effects on the temperature profile are related intimately to the BH spin, resulting in the variation of the value and the position of the peak temperature. It turns out that the value range of the colour temperature of the disc is extended by the MC effects.

We discuss jet production from an advection dominated accretion flow (ADAF) around a rotating black hole (BH) in an electromagnetic regime. An analytical expression for the jet power is derived by using an equivalent circuit in the BH magnetosphere. It turns out that a large fraction of jet powers is contributed from the inner region of the ADAF, and the jet power depends sensitively on the degree to which the flow is advection-dominated. In addition, we use our model to fit the strong jet powers of several BL Lac objects, which cannot be explained by virtue of the BZ process.

Using MHD perturbation, we derive the dispersion equation for pulsational instability of thin isothermal accretion disks. The effects of magnetic field, radial viscous force and the causality-modified α-viscosity are examined. We find that magnetic field is a global destabilizing factor acting on the viscous mode and the two acoustic modes. Radial viscous force is a global stabilizing factor for the two acoustic modes. The causality-modified α-viscosity acts mainly in the inner disk: it is a stabilizing factor for the viscous mode and I-mode when there is no magnetic field, and is a destabilizing factor for the two acoustic modes when there is a magnetic field.

The entropy of a self-gravitating and radiating system confined to a spherical box (for two cases with and without a central black hole) is calculated using the equation of state of radiation near the black hole horizon, derived by Li Li-xin and Liu Liao. Unlike the result of Sorkin et al., the present result contains no divergence difficulties and the upper bound on the total entropy in the case with a central black hole is equal to the entropy of a black hole having the same mass. The following scenario is considered reasonable: a central black hole forms first, it then grows until all the radiation and matter falls into the black hole. The entropy of the system at any stage of the collapse is always less than the entropy of the final black hole, thus providing an explanation of the origin of the black hole entropy.

Some electromagnetic quantities in the black hole (BH) magnetosphere are discussed by considering the coexistence of the Blandford–Znajek process and the magnetic coupling process. These quantities are (i) flux of electromagnetic energy and angular momentum transferred between the BH and the disc, (ii) poloidal currents flowing on the horizon and disc, (iii) poloidal electric field on the horizon, (iv) toroidal magnetic field in the BH magnetosphere, and (v) voltage drop across the magnetic coupling region on the horizon. It turns out that these quantities are determined mainly by three parameters: (i) the positions relative to the corotation magnetic surface, (ii) the BH spin, and (iii) the power-law index for the variation of the magnetic field on the disc.

A unified model of magnetic extraction of spin energy from a black hole is discussed based on the theory of black hole magnetosphere. The magnetic extracting power is expressed by a unified formula, which is applicable to both the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process. The strength and characteristics of the BZ power and the MC power are compared in detail. In addition, the impedance matching condition for the BZ power is extended to the more general case.

The evolution characteristics and energy extraction of a rotating black hole are investigated by considering the magnetic coupling with the surrounding accretion disc. It is found that both the mass and spin of the black hole might be reduced by the joint effects of disc accretion and magnetic coupling, provided that the latter is stronger than the former. The efficiencies of the two energy mechanisms are calculated and compared to a variety of parameters. In addition, the validity of the laws of black hole thermodynamics is discussed.

Some interesting behaviour of accreting particles in the gap region between the horizon of the Kerr black hole and the inner edge of the surrounding disc is investigated. The following results are obtained. (i) Spacetime coincidence of the maximum of angular velocity of accreting particles and that of the black hole horizon is extended to the more general disc-accretion. (ii) The possibility is discussed of negative energy of accreting particles in prograde orbit inside the ergosphere of the Kerr black hole, which is surrounded by strong enough magnetic field.

A reverse condition of accretion flow and its constraints on black hole spin in the quasi-cycle are proposed. It is shown that the necessary condition for the quasi-cycle is that the closed magnetic field lines must dominate over the open ones at the horizon. The efficiency of converting accreted rest mass into radiation energy in the quasi-cycle is proved to increase with the strength of the magnetic transfer process. In addition, a general expression for the efficiency is derived.

Evolution of black hole (BH) accretion disks is investigated by a new approach, in which the evolution of the central BH can be derived in terms of BH spin directly, and the evolution characteristics of the concerning BH parameters are shown more easily and obviously. As an example, the unusual evolution characteristics of angular velocity of BH horizon and that of accreting particles at the inner edge of the disk are derived by considering the Blandford-Znajek process.

It is shown that evolution characteristics of black hole (BH) parameters in the pure disk-accretion are determined uniquely by BH spin parameter a*. Some unusual evolution characteristics of the parameters of BH accretion disks, such as angular velocity, temperature and event horizon radius, are investigated in both thin and thick disk-accretion. And the corresponding turning points, a*c, are derived. In addition, two characteristic functions describing the evolution of BH parameters are derived for thin and thick disks, respectively.

In this paper, we present a simplified model for magnetized neutrino-dominated accretion flow (NDAF) in which effect of black hole (BH) spin is taken into account by adopting a set of relativistic correction factor, and the magnetic field is parameterized as \beta, the ratio of the magnetic pressure to the total pressure. It is found that the disc properties are sensitive to the values of the BH spin and \beta, and more energy can be extracted from NDAF for the faster spin and lower \beta., Comment: 4 pages, 3 figures, accepted for publication in Science in China Series G

The remnant mass at the last stage of black hole evaporation is of the order of the Planck mass and the corresponding entropy is of the order of 2 πk B . On the basis of Bekenstein's work, I have derived that the minimum entropy increase when a black hole accretes matter is 2 πk B ; this gives a lower bound of the Planck mass on the mass accretable by a black hole, which corresponds again to a minimum black hole entropy of the order of 2 πk B . Moreover, the minimum entropy and the minimum entropy increase are not affected by gravitation, hence the above statements also hold in the eraly universe. Hence I propose the conjecture that black hole entropy is qunatized with quantum 2 πk B .

The evolution characters of angular velocity Ω h of central black holes of accretion disks (including thin and thick disks) are investigated by considering both accretion and the Blandford\|Znajek (B\|Z) process. It is shown that the rate of change of Ω h with respect to time turns from the positive value to the negative, as the dimensionless angular momentum a\-* evolves to a critical value. Evolving in a non\|monotonous way, Ω h increases at first, and then decreases in a prograde accretion process. Therefore there exists a maximum of Ω h. It is pointed out that dimensionless angular momentum a \-* is more appropriate to describe the spinning state of a central black hole of an accretion disk than angular momentum J and angular velocity Ω h. PACC: 9760L; 0420