Unifying Penrose Process and Blandford–Znajek Mechanism Using Negative Phase Velocity

The extraction of rotational energy from a Kerr black hole admits several celebrated descriptions, including the Penrose process, wave superradiance, and the Blandford-Znajek mechanism. Traditionally treated as distinct, these processes are shown here to be unified through a single criterion: the existence of negative Killing energy flux across the horizon, locally manifested as negative phase velocity (NPV) in the ergosphere. I demonstrate that (i) the Penrose process corresponds to particle trajectories with Eχ < 0, (ii) superradiance corresponds to wave modes with ω < mΩH, and (iii) the Blandford–Znajek mechanism corresponds to electromagnetic field lines with ΩF < ΩH. In all cases, the horizon absorbs negative energy while positive energy escapes to infinity. By expressing these mechanisms through the NPV condition S · k < 0, I present a unified theoretical framework for black hole energy extraction.