The Penrose Process

Abstract

The Penrose process is a theoretical mechanism by which energy can be extracted from a rotating black hole. This possibility arises in the Kerr spacetime, where the existence of an ergoregion allows for asymptotic negative-energy states to exist. In this work, we study how these states allow part of the rotational energy of the black hole to be extracted when an infalling particle splits inside the ergoregion. We show that the maximum relative energy gain of the process (with respect to the infalling particle) is ΔE ≈ 0.207. The process is shown to be possible only under specific physical restrictions. The area theorem shows that this extraction cannot continue indefinitely, but only until the black hole has lost its rotational energy, while the horizon area does not decrease. The Wald and Bardeen-Press-Teukolsky inequalities further show that the process requires highly relativistic conditions: the decay products must have velocity |v| ≥ 1 2 c and relative velocity |w| ≥ 1 2 c.