Energy Extraction from Loop Quantum Black Holes: The Role of Magnetic Penrose Process and Quantum Gravity Effects with Astrophysical Insights

In this study, we explore the influence of quantum gravitational corrections, derived from Loop Quantum Gravity (LQG), on the efficiency of the magnetic Penrose process (MPP) in black hole (BH) environments. We begin by analyzing the rotating Loop Quantum Black Hole (LQBH) metric, describing the structure of the event horizon and ergosphere as functions of the quantum parameter $\epsilon = \gamma \delta$, with $\gamma$ representing the Immirzi parameter and $\delta$ the polymeric parameter, and the spin parameter $a$. These modifications provide a novel setting for exploring the dynamics of charged particles near the LQBH and evaluating the resultant energy extraction through the MPP. Interestingly, for a given value of the LQBH parameter $a$, we observe that the ergosphere region of the LQBH exhibits a more intricate structure compared to its classical counterpart, the Kerr BH, as $\epsilon$ increases. Furthermore, we find that the overall efficiency of the process decreases with $\epsilon$ that decreases $a_{max}$, again in contrast to the Kerr BH, where efficiency rises with an increasing $a$. Our analysis also extends to astrophysical contexts, applying constraints on the mass and magnetic field of LQBHs for astrophysical BH candidates, including SgrA*, M87*, NGC 1052, and BZ (Blandford and Znajek sources, i.e., supermassive BHs with masses around $10^9 M_\odot$ and magnetic fields in the range $10^3-10^4 \text{G}$). We assess these sources as potential accelerators of high-energy protons across different values of the quantum parameter $\epsilon$. Additionally, we examine how variations in the magnetic field strength $B$ and quantum corrections impact the energy of protons accelerated from M87$^{\star}$ and Sgr A$^{\star}$ following beta decay.