Analytic properties of force-free jets in the Kerr spacetime- I

Blandford-Znajek (BZ) mechanism describes a process extracting rotation energy from a spinning black hole (BH) via magnetic field lines penetrating the event horizon of central BH. In this paper, we present a perturbation approach to study force-free jets launched by the BZ mechanism, and its two immediate applications: (1) we present a high-order split monopole perturbation solution to the BZ mechanism, which accurately pins down the energy extraction rate $\dot E$ and well describes the structure of BH magnetosphere for all range of BH spins ($0\leq a\leq 1$); (2) the approach yields an exact constraint for the monopole field configuration in the Kerr spacetime, $I = Ω(1-A_ϕ^2)$, where $A_ϕ$ is the $ϕ-$component of the vector potential of electromagnetic field, $Ω$ is the angular velocity of magnetic field lines and $I$ is the poloidal electric current. The constraint is of particular importance to benchmark the accuracy of numerical simulations.

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