Thermodynamic fingerprints of quantum gravity: Bose gas analysis near string-cloud black holes

In this theoretical investigation, we explored the physical landscape where three fundamental domains of modern physics converge: black hole thermodynamics, quantum gravitational effects through the Generalized Uncertainty Principle (GUP), and the gravitational influence of cosmic string clouds. We examined a Bose gas system confined within a thin shell near a Schwarzschild black hole horizon and discovered how spacetime curvature, modified by both GUP corrections and string cloud effects, fundamentally transforms conventional thermodynamic behavior. Our detailed analysis revealed significant departures from classical flat spacetime thermodynamics, most notably the emergence of higher-order Formula: see text corrections to the Stefan–Boltzmann law that become increasingly dominant during late-stage black hole evaporation processes. We identified a critical extremum temperature that depends explicitly on the GUP parameter while remaining remarkably independent of the string cloud parameter. This finding, combined with our demonstration of nonnegative extremum pressure and entropy values, provides theoretical evidence supporting the black hole remnant hypothesis as a potential resolution to the information paradox. Furthermore, we discovered that the Formula: see text term in our modified thermodynamic equations suggests a special cooling mechanism that could fundamentally regulate black hole temperature evolution during the final stages of evaporation. Our results demonstrate how quantum gravitational effects and topological defects collectively reshape the thermodynamic landscape near event horizon.