The Blandford–Znajek Process for an Accelerating Kerr Black Hole

We investigate the Blandford–Znajek process for an accelerating Kerr black hole described by the neutral rotating C-metric. In contrast with the usual asymptotically flat problem, the stationary magnetosphere lies between a black-hole horizon and an acceleration horizon. We derive the stationary, axisymmetric force-free stream equation in closed form and show that the overall conformal factor of the spacetime drops out of the electromagnetic problem. Requiring regularity at both future horizons determines the leading split-monopole solution: the magnetic field lines rotate at the mean rate of the two horizons, while the current is driven by their relative rotation. Consequently, the acceleration horizon suppresses the total extracted power. At the same time, the angular distortion associated with acceleration distributes the luminosity unequally between the two hemispheres, producing intrinsically asymmetric jets even when their unsigned magnetic fluxes are equal. The leading calculation is perturbative only in the black-hole rotation and retains the full allowed acceleration dependence. At the next rotational order, the flux equation separates into a weighted angular eigenvalue problem and independent radial boundary-value equations. This reduction establishes uniqueness of the regular correction, recovers the known Kerr sector when the acceleration is removed, and explains why a finite elementary angular ansatz is unavailable in the accelerated geometry. The fixed-acceleration slow-rotation expansion is not uniform when the horizon separation becomes comparable to the square of the spin; that near-coalescence regime requires a separate double-scaled solution.

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