Quantum-Corrected Black Hole Solutions from f(R) Gravity and Their Canonical Ensemble Analysis

Abstract: This study investigates quantum-corrected black hole solutions derived from f(R) gravity and explores their thermodynamic properties using the canonical ensemble framework. By incorporating higher-order f(R) corrections into classical black hole metrics, we construct regular black hole solutions that eliminate classical singularities. Advanced canonical ensemble techniques, including path integral formulations and stability analyses, are employed to examine the thermodynamic stability, phase transitions, and critical phenomena of these f(R)-corrected black holes. The results indicate that f(R) corrections significantly alter the thermodynamic landscape, introducing novel phase structures and stability conditions. Additionally, numerical simulations are conducted to visualize the behavior of thermodynamic quantities under varying f(R) correction parameters. This work provides deeper insights into the interplay between modified gravity effects and black hole thermodynamics, contributing to the broader understanding of gravitational phenomena in strong gravitational fields.