A Class of Exact Solution to the Blandford-Znajek Process

Abstract

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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References in corpus (3)

• Total and Jet Blandford-Znajek Power in Presence of Accretion Disk
• Electrodynamics of black hole magnetospheres
• Analytic Solutions to the Constraint Equation for a Force-Free Magnetosphere around a Kerr Black Hole

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