Electrodynamics of the event horizon.

Abstract

This paper is an investigation of the electrodynamics of the event horizon of a Kerr black hole. It is demonstrated that the event horizon behaves quite generally as an asymptotic vacuum infinity for axisymmetric, charge-neutral, accreting electromagnetic sources. This is in contrast with the general notion that the event horizon can be treated as an imperfect conductive membrane with a surface impedance of 4\ensuremath{\pi}/c. The conductive-membrane model has been incorporated into the more sophisticated membrane paradigm of Thorne, Price, and Macdonald by supplementing the model with the full equations of general relativity. In certain situations (in particular those of astrophysical interest), the conductive-membrane interpretation forms the appropriate set of pictures and images in the membrane paradigm. In this paper we reevaluate the specific gedanken experiments that were originally used to motivate the paradigm. We find that great care must be exercised if the detailed interaction of a black hole's external gravitational field with a magnetized plasma is modeled by the electrodynamics of the conductive horizon membrane. For ingoing flows of plasma or electromagnetic waves (when the hole is passively accepting information), the interpretation of the horizon as a vacuum infinity is equivalent to an imperfect conductor with a surface impedance of 4\ensuremath{\pi}/c (the impedance of the vacuum). In situations when an imperfect conductor should radiate information (such as a Faraday wheel) the event horizon cannot, since it is an infinity. The event horizon does not behave quite generally as an imperfect conductor, but has electrodynamic properties unique to itself.