Analytic Solutions to the Constraint Equation for a Force-Free Magnetosphere around a Kerr Black Hole

Abstract

The Blandford-Znajek constraint equation for a stationary, axisymmetric black-hole force-free magnetosphere is cast in a 3+1 absolute space and time formulation, following Komissarov (2004). We derive an analytic solution for fields and currents to the constraint equation in the far-field limit that satisfies the Znajek condition at the event horizon. This solution generalizes the Blandford-Znajek monopole solution for a slowly rotating black hole to black holes with arbitrary angular momentum. Energy and angular momentum extraction through this solution occurs mostly along the equatorial plane. We also present a nonphysical, reverse jet-like solution.

6 pages, accepted for publication in ApJ

References in corpus (3)

• Electrodynamics of black hole magnetospheres
• Simulations of Jets Driven by Black Hole Rotation
• Force-Free Magnetosphere of an Accretion Disk -- Black Hole System. II. Kerr Geometry

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