Electric Charge and Magnetic Flux on Rotating Black Holes in a Force-Free Magnetosphere

The magnetosphere about rotating black holes surrounded by a magnetized accretion disk is expected to be largely force-free. In the recently discussed axisymmetric field-configuration of Gosh (1999), this naturally gives rise to a charge on the black hole of the order of BJ , as expected by dimensional analysis and a commensurate horizon flux of about BM. For stellar mass black holes surrounded by strong magnetic fields ∼ 10G, an electric charge of BJ is extremely small compared to the extremal charge M , so that the Kerr geometry remains a valid approximation for a force-free magnetosphere. This electric charge is similar to that of a magnetar. We interpret this to indicate that newly formed black holes from stellar collapse are endowed with an electric charge of about BJ , remaining far removed from extremality. Subject headings: black hole physics –magnetic fields The extraction of the rotational energy of a black hole using the magnetic field in the environment has been discussed as a possible way of powering AGN, as proposed by Blandford and Znajek(1977). These ideas have recently been contemplated in the context of gamma-ray bursts, where a low mass black hole is threaded by a magnetic flux of similar magnitude (Meszaros and Rees 1997; Paczynski 1998; van Putten 1999, 2000; Lee, Wijers and Brown 2000). In the Blandford-Znajek process, the plasma surrounding the black hole is assumed to be force-free. The electric field configuration is then determined by the magnetic field using the force-free condition. It turns out as discussed below that the electric field has non-vanishing normal component to the horizon. This can be interpreted in terms of a surface charge density on horizon in the frame work of the membrane paradigm developed