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

TL;DR

The paper investigates energy extraction from a rotating black hole embedded in a uniform electromagnetic field described by the exact Kerr-Bertotti-Robinson (KBR) metric. Using a Hamiltonian framework for charged particles and the exact electromagnetic potential, it analyzes the Magnetic Penrose Process (MPP) in this non-perturbative setting. A key finding is that the horizon and ergoregion respond non-monotonically to the intrinsic magnetic field $B$, which in turn induces a non-monotonic MPP efficiency, including regimes where the efficiency exceeds unity for suitable charge configurations. Applying the results to Sgr A*, the authors show that electrons can be accelerated up to $5\times 10^{15}$ eV near the horizon, with radiative losses reducing the energies to the observed TeV scale; this work underscores how spacetime-magnetic field coupling qualitatively reshapes BH energetics and energy-extraction prospects.

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.

Figures (8)

• Figure 1: Parameter space of the KBR BH in the $(a,B)$ plane. The shaded regions indicate the sign of the discriminant $D$ of the radial function $\Delta$: the region with $D>0$ corresponds to BHs with two horizons, $D=0$ marks the extremal curve (shown as a white solid line) and $D<0$ corresponds to configurations without horizons.
• Figure 2: Event horizon and static limit surface (ergosphere) of the KBR BH for different values of the spin parameter $a$ and magnetic field parameter $B$ are shown in the $x-z$ plane. Along each row, the parameter $B$ increases while the spin parameter $a$ is held fixed; along each column, the parameter $a$ increases for a fixed value of $B$. The black region denotes the event horizon, while the coloured region between the horizon and the static limit marks the ergoregion. Red colour indicates the maximum ergoregion thickness near the equator, gradually shifting to blue as it decreases toward the poles.
• Figure 3: Top left panel: Angular dependence of the static limit surface $r_{\rm sl}(\theta)$ for different values of the $B$ parameter at fixed spin $a=0.8$. Top right panel: shows the angular dependence of the static limit surface $r_{\rm sl}(\theta)$ for different values of the spin parameter $a$ at fixed spin $B$. Bottom left panel: Equatorial static limit radius $r_{\rm sl}(\theta=\pi/2)$ across the $(a,B)$ parameter space. Bottom-right panel: Equatorial static limit radius $r_{\rm sl}(\theta=\pi/2)$ and horizon radius $r_{\rm h}$ as a function of parameter $B$ for different values of spin parameter $a$.
• Figure 4: Left panel: Radial profile of the effective potential $V_{\text{eff}}$ for different values of the magnetic field $B$. Right panel: Radial profiles of $\Omega_{+}$, $\Omega_{-}$, and $\Omega$ for different values of the magnetic field $B$. Solid lines correspond to $\Omega_{-}$, dashed lines to $\Omega_{+}$, and dotted lines to $\Omega$.
• Figure 5: Efficiency distribution of energy extraction via the MPP for the KBR BH. The left panel shows the case $q_3/m_1 = 0$, while the right panel corresponds to $q_3/m_1 = -2$. The magnetic field parameter is fixed at $B = 0.05$.