Maximum efficiency of the collisional Penrose process

TL;DR

This paper analyzes the maximum efficiency of the collisional Penrose process near extremal rotating black holes, deriving bounds on energy extraction efficiency and applying the results to Kerr-Newman and Kerr black holes.

Contribution

It establishes bounds on the efficiency of the collisional Penrose process for different particle mass scenarios near extremal black holes.

Findings

Maximum efficiency for finite mass particles is less or equal to that for heavy particles.

Efficiency bound is η=3 for Kerr-Newman black holes.

Results reproduce recent findings for Kerr black holes.

Abstract

We consider collision of two particles that move in the equatorial plane near a general stationary rotating axially symmetric extremal black hole. One of particles is critical (with fine-tuned parameters) and moves in the outward direction. The second particle (usual, not fine-tuned) comes from infinity. We examine the efficiency $\eta $ of the collisional Penrose process. There are two relevant cases here: (i) a particle falling into a black hole after collision is heavy, (ii) it has a finite mass. We show that the maximum of $\eta $ in case (ii) is less or equal to that in case (i). It is argued that for superheavy particles, the bound applies to nonequatorial motion as well. As an example, we analyze collision in the Kerr-Newman background. When the bound is the same for processes (i) and (ii), $\eta =3$ for this metric. For the Kerr black hole, recent results in literature are reproduced.