Quantum Gravity Corrections to Black Hole Thermodynamics: Modified Hawking Radiation and Accretion Disk Physics

Black holes represent fundamental laboratories for testing quantum gravity theories, where extreme curvature and thermal physics provide unique opportunities to probe Planck-scale modifications to space time. We investigate quantum gravity corrections to black hole thermodynamics through the Generalized Uncertainty Principle (GUP), focusing on modifications to Hawking radiation and accretion disk physics. Our comprehensive analysis reveals that GUP effects systematically alter the temperature-mass relationship for black holes, leading to observable signatures in both the thermal emission spectrum and accretion disk properties. Through detailed calculations incorporating relativistic effects and advanced statistical mechanics, we demonstrate that quantum gravity modifications introduce spectral distortions in the X-ray regime that are potentially detectable with current and future high-energy missions. The modified thermodynamics also affects accretion efficiency, disk temperature profiles, and iron line emission, producing characteristic signatures in the observed continuum spectra. Our analysis of recent data from NuSTAR, XRISM, and other X-ray observatories places new constraints on the GUP parameter β≤1500 for stellar-mass black holes, representing the most stringent limits from black hole observations to date. These results demonstrate the potential for black hole observations to probe fundamental quantum gravity effects and provide complementary constraints to those derived from neutron star studies. The framework developed here establishes black hole systems as viable laboratories for testing quantum gravity theories through multi-messenger astronomy.