Using numerical simulations, we modeled the general relativistic magnetohydrodynamic behavior of a plasma flowing into a rapidly rotating black hole in a large-scale magnetic field. The results show that a torsional Alfvén wave is generated by the rotational dragging of space near the black hole. The wave transports energy along the magnetic field lines outward, causing the total energy of the plasma near the hole to decrease to negative values. When this negative energy plasma enters the horizon, the rotational energy of the black hole decreases. Through this process, the energy of the spinning black hole is extracted magnetically

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To investigate the formation mechanism of relativistic jets in active galactic nuclei and microquasars, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the Ðrst numerical simulations of jet formation in a rapidly rotating (a \ 0.95) Kerr black hole magnetosphere. We study cases in which the Keplerian accretion disk is both corotating and counterrotating with respect to the black hole rotation, and investigate the Ðrst D50 light-crossing times. In the corotating disk case, our results are almost the same as those in Schwarzschild black hole cases : a gas pressureÈdriven jet is formed by a shock in the disk, and a weaker magnetically driven jet is also generated outside the gas pressureÈdriven jet. On the other hand, in the counter-rotating disk case, a new powerful magnetically driven jet is formed inside the gas pressureÈdriven jet. The newly found magnetically driven jet in the latter case is accelerated by a strong magnetic Ðeld created by frame dragging in the ergosphere. Through this process, the magnetic Ðeld extracts the energy of the black hole rotation.

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The radio observations have revealed the compelling evidence of the existence of relativistic jets not only from active galactic nuclei but also from "microquasars" in our Galaxy. In the cores of these objects, it is believed that a black hole exists and that violent phenomena occur in the black hole magnetosphere, forming the relativistic jets. To simulate the jet formation in the magnetosphere, we have newly developed the general relativistic magnetohydrodynamic code. Using the code, we present a model of these relativistic jets, in which magnetic fields penetrating the accretion disk around a black hole play a fundamental role of inducing nonsteady accretion and ejection of plasmas. According to our simulations, a jet is ejected from a close vicinity to a black hole (inside , where is the Schwarzschild radius) at a maximum speed of ∼90% of the light velocity (i.e., a Lorentz 3r r S S factor of ∼2). The jet has a two-layered shell structure consisting of a fast gas pressure-driven jet in the inner part and a slow magnetically driven jet in the outer part, both of which are collimated by the global poloidal magnetic field penetrating the disk. The former jet is a result of a strong pressure increase due to shock formation in the disk through fast accretion flow ("advection-dominated disk") inside 3r S , which has never been seen in the nonrelativistic calculations.

The mechanism of solar coronal heating has been unknown since the discovery that the coronal plasma temperature is a few million degrees. There are two promising mechanisms, the Alfvén wave model and the nanoflare-reconnection model. Recent observations favor the nanoflare model since it readily explains the ubiquitous small-scale brightenings all over the Sun. We have performed magnetohydrodynamic (MHD) simulations of the nonlinear Alfvén wave coronal heating model that include both heat conduction and radiative cooling in an emerging flux loop and found that the corona is episodically heated by fast-and slow-mode MHD shocks generated by nonlinear Alfvén waves via nonlinear mode-coupling. We also found that the time variation of the simulated extreme-ultraviolet and X-ray intensities of these loops, on the basis of the Alfvén wave model, is quite similar to the observed one, which is usually attributed to nanoflare or picoflare heating. This suggests that the observed nanoflares may not be a result of reconnection but in fact may be due to nonlinear Alfvén waves, contrary to current widespread opinion.

We demonstrate that the formation of collapsing cores in subcritical clouds is accelerated by nonlinear flows, by performing three-dimensional non-ideal MHD simulations. An initial random supersonic (and trans-Alfvénic) turbulent-like flow is input into a self-gravitating gas layer that is threaded by a uniform magnetic field (perpendicular to the layer) such that the initial mass-to-flux ratio is subcritical. Magnetic ambipolar diffusion occurs very rapidly initially due to the sharp gradients introduced by the turbulent flow. It subsequently occurs more slowly in the traditional near-quasistatic manner, but in regions of greater mean density than present in the initial state. The overall timescale for runaway growth of the first core(s) is several × 10 6 yr, even though previous studies have found a timescale of several × 10 7 yr when starting with linear perturbations and similar physical parameters. Large-scale supersonic flows exist in the cloud and provide an observationally testable distinguishing characteristic from core formation due to linear initial perturbations. However, the nonlinear flows have decayed sufficiently that the relative infall motions onto the first core are subsonic, as in the case of starting from linear initial perturbations. The ion infall motions are very similar to those of neutrals; however, they lag the neutral infall in directions perpendicular to the mean magnetic field direction and lead the neutral infall in the direction parallel to the mean magnetic field.