Non-Monotonic Enhancement of the Magnetic Penrose Process in Kerr-Bertotti-Robinson Spacetime and its Implication for Electron Acceleration

TL;DR

This paper investigates how the magnetic Penrose process's efficiency in Kerr-Bertotti-Robinson spacetime varies non-monotonically with magnetic field strength, revealing maximum energy extraction and electron acceleration up to ultra-high energies.

Contribution

It demonstrates the non-monotonic behavior of the ergoregion and energy extraction efficiency in KBR spacetime and applies this to estimate electron energies near supermassive black holes.

Findings

Energy extraction efficiency peaks at intermediate magnetic fields.

Electrons can be accelerated up to 10^{15} eV near SgrA*.

Radiative losses can reduce electron energies to observed TeV scales.

Abstract

We studied the magnetic Penrose process (MPP) in the Kerr-Bertotti-Robinson (KBR) spacetime, an exact rotating electrovacuum solution describing a black hole (BH) immersed in an intrinsic, uniform electromagnetic field. We analyze the behavior of charged particles in this geometry and find that the spacetime structure itself responds non-monotonically to the background magnetic field $B$. Specifically, both the event horizon and the static limit surface first expand as $B$ increases, reach a maximum size at an intermediate field strength, and then contract toward the extremal limit. Although the ergoregion itself shrinks monotonically with $B$, this structural feature gives rise to a pronounced non-monotonic dependence of the energy extraction efficiency on the magnetic field $B$, i.e., the efficiency initially rises, attains a maximum value, and subsequently falls as the extremal condition is approached. This contrasts sharply with the monotonic trends usually associated with magnetic enhancements in the Kerr geometry. We further explore an astrophysical application of the MPP by estimating the maximum energy of electrons escaping from the ergoregion of the KBR BH. Modeling neutron beta decay occurring near the event horizon, we derive an analytical expression for the energy gained by electrons accelerated by the magnetic field. Applying our results to the supermassive BH at the Galactic center, $\mathrm{SgrA}^*$, we find that electrons can be accelerated up to energies of $\sim 10^{15}\,\mathrm{eV}$ for realistic values of the spin and magnetic field. Although these energies exceed the observed upper range of cosmic-ray electrons, radiative losses such as synchrotron emission and inverse-Compton scattering can efficiently reduce them to the observed $\mathrm{TeV}$ scale.