Astrophysical signatures of Konoplya-Zhidenko black holes: Gravitational lensing and thermodynamics

This study investigates the astrophysical implications of deformed black hole geometries, specifically focusing on the Konoplya-Zhidenko (KZ) metric which introduces parametric deviations to the standard Schwarzschild solution. We analyze how the deformation parameter eta modifies key physical properties across multiple domains: thermodynamic behavior, gravitational lensing characteristics, and quantum-corrected entropy. Our results demonstrate that even modest deviations from general relativity produce significant alterations in Hawking temperature profiles, event horizon structure, and black hole stability conditions. Through application of the GB theorem, we derive weak deflection angles in vacuum and plasma environments, revealing enhanced gravitational lensing effects particularly prominent at small impact parameters. The inclusion of exponential correction entropy formalism further elucidates how quantum modifications influence critical thermodynamic quantities including internal energy, Helmholtz free energy, and heat capacity. Additionally, using the Jacobi metric approach, we extend our analysis to massive particles, showing that velocity-dependent corrections to deflection angles emerge naturally from the deformed geometry. These findings collectively contribute to a more comprehensive understanding of modified gravity theories and establish a theoretical framework for empirical verification through high-precision astrophysical observations of black hole systems.