Remarks on electrical Penrose process for magnetized Reissner-Nordstr\"om black hole

TL;DR

This paper investigates how external magnetic fields influence energy extraction from magnetized Reissner-Nordström black holes via the electric Penrose process, deriving conditions for ergosphere formation and efficiency.

Contribution

It extends previous analyses by providing analytical expressions for critical magnetic fields and clarifies the magnetic field's role in energy extraction efficiency.

Findings

Magnetic fields induce ergospheres enabling energy extraction.

Derived expressions for critical magnetic fields controlling the process.

External magnetic fields can enhance or suppress energy extraction.

Abstract

The energy extraction from a magnetized Reissner-Nordstr\"om black hole is analyzed within the framework of the electric Penrose mechanism. The presence of an external magnetic field induces an axisymmetric configuration and an ergosphere (the region where energy extraction is possible) arises, allowing for negative energy states even in an otherwise static spacetime. By analyzing the decay of particles at turning points of the radial motion, we derive the general expression for the efficiency of the process in terms of the metric coefficients and the electromagnetic potential. This formulation provides a direct criterion for identifying the ergoregions and we show that the magnetic field acts as a control parameter that governs both the configuration of the ergosphere and the efficiency of the process. In particular, analytical expressions for the critical magnetic fields that determine the onset and suppression of energy extraction are determined. Our results extend previous analysis of the electric Penrose process for magnetized configurations and clarify the role of the external field in enhancing or inhibiting energy extraction from charged black holes.