Blandford-Znajek mechanism in the general stationary axially-symmetric black-hole spacetime

TL;DR

This paper generalizes the Blandford-Znajek mechanism to arbitrary axially symmetric black-hole spacetimes, deriving formulas for magnetic flux and energy extraction rate that depend on a single deformation parameter.

Contribution

It provides a new framework to analyze electromagnetic energy extraction from deformed black holes beyond the Kerr solution.

Findings

Formulas for magnetic flux and energy extraction rate applicable to general axially symmetric black holes.

Dependence of energy extraction on a single deformation parameter in the dominant order.

Extension of Blandford-Znajek process analysis beyond Kerr spacetime.

Abstract

We consider the Blandford-Znajek process of electromagnetic extraction of energy from a general axially symmetric asymptotically flat slowly rotating black hole. Using the general parametrization of the black-hole spacetime we construct formulas for the flux of the magnetic field and the rate of energy extraction, which are valid not only for the Kerr spacetime, but also for its arbitrary axially symmetric deformations. We show that in the dominant order these quantities depend only on a single deformation parameter, which relates the spin frequency of a black hole with its rotation parameter.