Recursive Penrose processes in electrically charged black hole spacetimes: Backreaction and energy extraction

TL;DR

This paper investigates a recursive energy extraction process from charged black holes in AdS spacetime, accounting for backreaction, and finds it results in finite energy gain without causing instability or violating cosmic censorship.

Contribution

It introduces a detailed analysis of recursive Penrose processes with backreaction in charged AdS black holes, revealing finite energy extraction limits and the role of confinement.

Findings

Energy extraction is finite due to backreaction effects.

The process terminates with a neutral or nearly neutral black hole.

No black hole bomb instability occurs in this setup.

Abstract

We study a recursive Penrose process and the energy extraction for the decay of electrically charged particles in a Reissner-Nordstr\"om black hole spacetime with anti-de Sitter (AdS) asymptotics, incorporating the backreaction on the black hole's mass and charge. A recursive process requires that the decay products are confined in a finite region so that the emitted particles bounce back for further decay. In AdS spacetimes, the confinement arises naturally. Outgoing particles encounter a turning point and are reflected. One may impose a mirror at finite radius, but in AdS, backreaction makes these two confinement methods equivalent. Let $Q_n$ be the black hole charge after $n$ decays, and define $n_{\rm c}$ as the index for which the black hole's charge is zero, $Q_{n_{\rm c}}=0$. For $n_{\rm c}$ integer the black hole's charge decreases and reaches exactly zero after a finite number of decays, terminating the process. However, the last particle turns back, and encountering zero charge, falls into the hole. The final state is a charged black hole whose charge equals the sum of the original black hole and the initial particle charges. For $n_{\rm c}$ noninteger, the black hole charge decreases and can be arbitrarily small, but is never zero. The last allowed decay occurs at $n=n_{c}^-$, where $n=n_{c}^-$ is the greatest integer less than $n_{\rm c}$. Any further decay invalidates the approximations, the particles would carry a charge comparable to the black hole mass, transforming the problem into a two-body problem. The would-be subsequent decay would violate cosmic censorship and the process terminates before any inconsistency arises. In the integer and noninteger cases, the system yields a finite energy gain. Backreaction ensures that the process extracts a finite amount of energy. No black hole bomb occurs, the system works at most as an energy factory.