A Class of Exact Solution to the Blandford-Znajek Process

Details A Class of Exact Solution to the Blandford-Znajek Process A Class of Exact Solution to the Blandford-Znajek Process

2005-11-22

arxiv.org/abs/astro-ph/0511661v1

Gen.Rel.Grav.39:785-794,2007

Astronomy and Astrophysics

Astrophysics

8 pages, no figures

Scientific paper

10.1007/s10714-007-0418-2

We analyze the constraint equation giving allowed solutions describing fields and currents in a force-free magnetosphere around a rotating black hole. Utilizing the divergence properties of the energy and angular-momentum fluxes for physically allowed solutions, we conclude that poloidal surfaces are independent of the radial coordinate for large values of $r$. Using this fact and the Znajek regularity condition, we explicitly derive all possible exact solutions admitted by the constraint equation for $r$ independent poloidal surfaces, which are given in terms of the electromagnetic angular velocity function $\Omega = 1/a\sin^2\theta$, where $a$ is the angular momentum per unit mass of the black hole.

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