Dynamo effect of spacetime curvature in force-free magnetospheres

Abstract

We study the possibility of growth of the electric and magnetic fields in a force-free plasma due strictly to the gravitational curvature of the spacetime domain where those fields lie. To this end, we identify a total energy by analogy with the results of classical magnetohydrodynamics. After obtaining the general evolution equation for the total energy, we apply to it to the fiducial observers in a number of classical metrics: Schwarzschild, Boyer-Lindquist, Kerr-Schild, Robertson-Walker, and post-Newtonian approximation. As a rule the shift velocity plays the role of minus the fluid velocity in Newtonian MHD, but the details are often highly intricate.