Magnetic extraction of black hole rotational energy: Method and results of general relativistic magnetohydrodynamic simulations in Kerr space-time

We present the complete numerical method of general relativistic magnetohydrodynamic simulations in Kerr space-time, and then apply those techniques to the basic astrophysical problem of activity near a Kerr black hole immersed in a plasma with a large-scale magnetic field. Our numerical results show that a torsional Alfven wave is generated in the ergosphere of the Kerr black hole. This wave propagates outward along the magnetic field lines, extracting rotational energy from the plasma in the ergosphere. If the magnetic field is strong enough, the plasma energy in the ergosphere rapidly decreases and eventually becomes negative. When this negative energy plasma is swallowed by the black hole, the total energy of the black hole decreases, spinning it down. This energy extraction mechanism is similar to the ''Penrose process,'' in which the negative energy also plays an important role. The difference between the two is the force that causes the redistribution of the angular momentum (which is necessary to produce the negative energy). In the Penrose process, elementary particle interactions cause the redistribution, while in the present case it is performed by magnetic tension