The magneto-rotational (Balbus-Hawley) instability in Kerr spacetime is investigated on a 3+1 viewpoint. The linear equations for perturbations have been described in a Keplerian orbiting observer's frame. The universal upper bound to the growth rate of the magneto-rotational instability, which exists in the Newtonian case, is changed by the rotation of spacetime. It is shown that a rapid instability is generated due to a large differential rotation of spacetime. The "gravito-magnetic force" produces a high exchange frequency of angular momentum. In the case of the extreme Kerr spacetime, the maximum growth rate normalized by the proper period reaches 4× 2π at the radius of the marginally stable orbit rms. This rate is five times the Newtonian one. The critical wavenumber for an unstable mode is determined by the shear coupled with the exchange frequency of angular momentum. The unstable range of wavenumber expands in proportion to the angular velocity of spacetime. In Schwarzschild spacetime, the growth rate and the range of wavenumber of the instability are nearly the same as the Newtonian ones. The rapid magneto-rotational instability drives a large generation of heat near the radius of the marginally stable orbit. The structure and dynamics of the standard accretion disk at the inner boundary rin=rms, may be greatly changed by the rapid magneto-rotational instability.
8th Asian-Pacific Regional Meeting, Volume II
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