Causal extraction of black hole rotational energy by various kinds of electromagnetic fields

Recent general relativistic magnetohydrodynamics (MHD) simulations have suggested that relativistic jets from active galactic nuclei (AGNs) have been powered by the rotational energy of central black holes. Some mechanisms for extraction of black hole rotational energy have been proposed, like the Penrose process, Blandford-Znajek mechanism, MHD Penrose process, and superradiance. The Blandford-Znajek mechanism is the most promising mechanism for the engines of the relativistic jets from AGNs. However, an intuitive interpretation of this mechanism with causality is not yet clarified, while the Penrose process has a clear interpretation for causal energy extraction from a black hole with negative energy. In this paper, we present a formula to build physical intuition so that in the Blandford-Znajek mechanism, as well as in other electromagnetic processes, negative electromagnetic energy plays an important role in causal extraction of the rotational energy of black holes.