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

Govind Menon·Charles D. Dermer
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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.

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Govind Menon, Charles D. Dermer. 2005-09-06. Analytic Solutions to the Constraint Equation for a Force-Free Magnetosphere around a Kerr Black Hole. https://doi.org/10.1086/497631

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