Quantum Gravity Inspired Thermodynamic and Optical Properties of Schwarzschild Black Holes with Radial Noncommutativity

We investigate the thermodynamic and optical properties of a Schwarzschild black hole within the framework of dynamical noncommutativity, in which the noncommutative parameter varies as a function of the radial coordinate. Interpreting this parameter as an effective quantum-gravitational smearing length, we construct a regular black hole geometry that interpolates smoothly between a quantum-affected core and the classical Schwarzschild spacetime at large distances. We analyze the horizon structure and derive modified expressions for the Hawking temperature, entropy, heat capacity, and free energy. Furthermore, we examine the implications for Hawking radiation and the black hole shadow, providing expressions for the spectral energy distribution and the total evaporation rate. Our results extend previous studies of noncommutative Schwarzschild black holes with constant noncommutativity, revealing new features in both the thermodynamic behavior and the associated optical signatures, including radiation spectra and event horizon shadows. These findings provide a coherent and consistent effective description of quantum gravity effects in black hole evaporation and optical properties.