ar X iv : a st ro - p h / 05 04 02 4 v 1 1 A pr 2 00 5 Magnetorotational Instability around a Rotating Black Hole
نویسندگان
چکیده
The magnetorotational instability(MRI) in the Kerr spacetime is studied on a 3+1 viewpoint. The Maxwell's equations are expressed in a circularly orbiting observer's frame that co-rotates with matter in Keplerian orbits. The hydromag-netic equations are represented in a locally nonrotating frame(LNRF). There exist large proper growth rates in MRI around a rapidly rotating black hole. The large " centrifugal force " and the rapid variations of magnetic fields are caused by the rotation of spacetime geometry. As the result, in the extreme Kerr case the maximum proper growth rate at r = r ms becomes about twelve times as large as that in Schwartzshield case, where r ms is the radius of a marginally stable orbit. The unstable range of wavenumber expands according to the rotational speed of spacetime geometry. The over stable mode of the instability becomes remarkable when the circular motion of the disk is quasi-relativistic and the strength of magnetic field is so large that the Alfven velocity is v A ≥ 0.1c. When the waves of perturbations propagate in the radial direction, these waves oscillate and their amplitudes grow exponentially. This instability is caused by the differential rotation of the circularly orbiting frame. The universality of the local Oort A-value of the disk is discussed in curved spacetime. In the extreme Kerr geometry, the amplitude of the maximum growth rate in the dynamical shear instability (DSI) reaches to infinity at r = r ms. The behaviors of maximum growth rates between MRI and DSI are remarkably different each other.
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