Consistent analytic approach to the efficiency of collisional Penrose process

TL;DR

This paper develops a consistent analytical method to evaluate the efficiency of the collisional Penrose process near maximally rotating Kerr black holes, revealing new upper limits and conditions for achieving high energy extraction.

Contribution

It introduces a unified analytic framework for the collisional Penrose process, clarifies previous discrepancies, and identifies conditions for maximum efficiency in particle collisions near black holes.

Findings

Maximum efficiency for ingoing fine-tuned particles is approximately 2.186.

Maximum efficiency for bounced-back fine-tuned particles is approximately 13.93.

High-efficiency collisions can occur with various particle types, including massless and highly relativistic particles.

Abstract

We propose a consistent analytic approach to the efficiency of collisional Penrose process in the vicinity of a maximally rotating Kerr black hole. We focus on a collision with arbitrarily high center-of-mass energy, which occurs if either of the colliding particles has its angular momentum fine-tuned to the critical value to enter the horizon. We show that if the fine-tuned particle is ingoing on the collision, the upper limit of the efficiency is $(2+\sqrt{3})(2-\sqrt{2})\simeq 2.186$, while if the fine-tuned particle is bounced back before the collision, the upper limit is $(2+\sqrt{3})^{2}\simeq 13.93$. Despite earlier claims, the former can be attained for inverse Compton scattering if the fine-tuned particle is massive and starts at rest at infinity, while the latter can be attained for various particle reactions, such as inverse Compton scattering and pair annihilation, if the fine-tuned particle is either massless or highly relativistic at infinity. We discuss the difference between the present and earlier analyses.