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

Abstract

Sandi Setiawan*

The extraction of rotational energy from a Kerr black hole admits several celebrated descriptions, including the Penrose process (Penrose (1969)), wave superradiance (Zel’dovich (1971), Misner (1972), Teukolsky, Press (1974); see also Thorne, Price, Wheeler (1986)), and the Blandford-Znajek mechanism (Blandford, Znajek (1977)). 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 (Setiawan, Mackay, Lakhtakia (2005)). We 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, we present a unified theoretical framework for black hole energy extraction.

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