Evolution characteristics of a Kerr black hole (BH) are investigated by considering the coexistence of disc accretion with the Blandford–Znajek process (the BZ process) and magnetic coupling of the BH with the surrounding disc (MC process). (i) The rate of extracting energy from the rotating BH in the BZ process and that in MC process are expressed by a unified formula, which is derived by using an improved equivalent circuit. (ii) The mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the disc is given in the context of general relativity and conservation of magnetic flux. (iii) The power and torque in the BZ process are compared with those in MC process in detail. (iv) Evolution characteristics of the BH and energy extracting efficiency are discussed by using the characteristic functions of BH evolution in the corresponding parameter space. (v) Power dissipation on the BH horizon and BH entropy increase are discussed by considering the coexistence of the above energy mechanisms.

Recent observations and theoretical work on gamma-ray bursts (GRBs) favor the central engine model of a Kerr black hole (BH) surrounded by a magnetized neutrino-dominated accretion flow (NDAF). The magnetic coupling between the BH and disk through a large-scale closed magnetic field exerts a torque on the disk, and transports the rotational energy from the BH to the disk. We investigate the properties of the NDAF with this magnetic torque. For a rapid spinning BH, the magnetic torque transfers enormous rotational energy from BH into the inner disk. There are two consequences: (i) the luminosity of neutrino annihilation is greatly augmented; (ii) the disk becomes thermally and viscously unstable in the inner region, and behaves S-Shape of the surface density versus accretion rate.It turns out that magnetically torqued NDAF can be invoked to interpret the variability of gamma-ray luminosity. In addition, we discuss the possibility of restarting the central engine to produce the X-ray flares with required energy.Subject headings: accretion, accretion disk-black hole physics -magnetic fieldsgamma rays: bursts -neutrinos Recently, the magnetic coupling (MC) between the central spinning BH and their surrounding accretion disk has been paid much attention (e.g. Blandford 1999;van Putten 1999;Li & Paczynski 2000;Li 2002;Wang et al. 2002). As a variant of the BZ process, the MC process exerts a torque on the disk, and transports the rotational energy from the BH to the disk. The effects of MC torque has been discussed in some disk models, for example, Lai (1998) and Lee (1999) in a neutron star with slim disk, Li (2002), Wang et al. (2002Wang et al. ( , 2003, Kluzniak and Rappaport (2007) in a compact object with thin disk, Ye et al. (2007) and Ma et al. (2007) in a BH with advection-dominated accretion flow (ADAF). It is found, the disk properties are greatly changed and its luminosity is augmented significantly due to the rotational energy of BH extracted in the MC process. Therefore, it is attractive for us to investigate the effects of MC torque on NDAF. To highlight the effects of MC torque, we ignore other MHD process, such as BZ and BP mechanism, and we refer to this model as MCNDAF.This paper is organized as follows. In Sect. 2 we describe the MCNDAF model, which is a relativistic steady state thin disk. The effects of MHD stress are described by the dimensionless parameter α. The main equations are based on DPN02 and NPK01.Recently, GLL06, Chen & Beloborodov (2006) and Shibata et al. (2006Shibata et al. ( , 2007 argued that the general relativistic (GR) effects are important for NDAF, so we introduce GR correction factors to the equations. The MC torque appears in the angular momentum equation.

Aims. An extreme Kerr black hole (BH) surrounded by a precessing disk is invoked to explain the light curves of gamma-ray bursts (GRBs) based on the coexistence of the Blandford-Znajek (BZ) and the magnetic coupling (MC) processes. Methods. The overall shape of the light curves and the duration of GRBs are interpreted by the evolution of the half-opening angle of the magnetic flux on the BH horizon, and the complex temporal structures are modulated by the precession and nutation of the jet powered by the BZ process. Results. The time profile of the emission exhibits a fast rise and a slow decay due to the effect of the evolution of the half-opening angle. The light curves of several GRBs are well fitted by this model with only six free parameters.

Effects of magnetic coupling (MC) of a rotating black hole (BH) with its surrounding accretion disk are discussed in detail in the following aspects: (i) The mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the disk is modified based on a more reasonable configuration of magnetic field, and a condition for coexistence of the Blandford-Znajek (BZ) and the MC process is derived. (ii) The transfer direction of energy and angular momentum in MC process is described equivalently by the co-rotation radius and by the flow of electromagnetic angular momentum and redshifted energy, where the latter is based on an assumption that the theory of BH magnetosphere is applicable to both the BZ and MC processes. (iii) The profile of the current on the BH horizon and that of the current density flowing from the magnetosphere onto the horizon are given in terms of the angular coordinate of the horizon. It is shown that the current on the BH horizon varies with the latitude of the horizon and is not continuous at the angular boundary between the open and closed magnetic field lines. (iv) The MC effects on disk radiation are discussed, and a very steep emissivity is produced by MC process, which is consistent with the recent XMM-Newton observation of the nearby bright Seyfert 1 galaxy MCG-6-30-15 by a variety of parameters of the BH-disk system.

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A B S T R A C TThe effects of the Blandford-Znajek (BZ) process on the evolution of the central black holes of accretion discs are investigated by an analytical method and numerical calculations in this paper. It is shown that the BZ process reduces the rates of change of some parameters of the black hole, such as mass, angular momentum, dimensionless angular momentum and temperature, and the evolution of the central black hole towards the extreme Kerr black hole is depressed effectively. However, the rate of change of entropy of the central black hole is augmented in the BZ process. In addition, the consistency of the BZ process with the three laws of black hole thermodynamics is discussed.