Confined Penrose process and black-hole bomb

TL;DR

This paper investigates particle decay processes within black hole ergospheres, demonstrating conditions under which energy can grow indefinitely, leading to a black-hole bomb, and clarifying scenarios where such explosive energy amplification is impossible.

Contribution

It introduces a detailed analysis of decay processes inside ergospheres, identifying conditions for energy amplification and the impossibility of black-hole bombs in certain scenarios.

Findings

Indefinite energy growth is possible with charged particles in Reissner-Nordström black holes.

Black-hole bombs are impossible with neutral particles in rotating black holes if decay occurs at the turning point.

A specific condition relates mass ratios and velocities for black-hole bombs to occur.

Abstract

We consider the decay of a particle with some energy $E_{0}>0$ inside the ergosphere of a black hole. After the first decay one of particles with the energy $E_{1}<0$ falls towards a black hole while the second one with $% E_{2}>E_{0}\,\ $moves in the outward direction. It bounces back from a reflecting shell and, afterwards, the process repeats. For radial motion of charged particles in the Reissner-Nordst\"{o}m metric, the result depends strongly on a concrete scenario. In particular, an indefinitely large growth of energy inside a shell is possible that gives rise to a black-hole bomb. We also consider a similar multiple process with neutral particles in the background of a rotating axially symmetric stationary black hole. We demonstrate that, if particle decay occurs in the turning point, a black-hole bomb in this case is impossible at all. For a generic point inside the ergoregion, there is a condition for a black-hole bomb to exist. It relates the ratio of masses before and after decay and the velocity of a fragment in the center of mass frame.