# Blandford-Znajek process in vacuo and its holographic dual

Jacobson, Ted (Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA) ; Rodriguez, Maria J. (Max Planck for Gravitational Physics, Potsdam 14476, Germany and Department of Physics, Utah State University, 4415 Old Main Hill Road, Utah 84322, USA)

11 June 2019

Abstract: Blandford and Znajek discovered a process by which a spinning black hole can transfer rotational energy to a plasma, offering a mechanism for energy and jet emissions from quasars. Here we describe a version of this mechanism that operates with only vacuum electromagnetic fields outside the black hole. The setting, which is not astrophysically realistic, involves either a cylindrical black hole or one that lives in $2+1$ spacetime dimensions, and the field is given in simple, closed form for a wide class of metrics. For asymptotically anti–de Sitter black holes in $2+1$ dimensions, the holographic dual of this mechanism is the transfer of angular momentum and energy, via a resistive coupling, from a rotating thermal state containing an electric field to an external charge density rotating more slowly than the thermal state. In particular, the entropy increase of the thermal state due to Joule heating matches the Bekenstein-Hawking entropy increase of the black hole.

Published in: Physical Review D 99 (2019)