Hawking radiation and gravitational lensing in quantum-modified black holes via the Gauss–Bonnet method

Abstract This paper investigates the effects of quantum-modified effective metrics on black hole (BH) physics, with a focus on Hawking radiation and gravitational lensing phenomena. We employ the Gauss–Bonnet theorem to derive the Hawking temperature and deflection angles in spacetimes incorporating quantum corrections parameterized by $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> . Our analysis reveals how these corrections modify the Hawking temperature, creating distinct temperature profiles that deviate from classical predictions. We extend our study to examine gravitational lensing of both massless and massive particles using the optical and Jacobi metric formalisms, demonstrating significant modifications to deflection angles relative to general relativity. Furthermore, we analyze how surrounding media specifically cold non-magnetized plasmas and axion-plasmon fields-further alter light propagation, introducing frequency-dependent effects that could serve as observational signatures of quantum gravity. We also present orbital precession predictions for S-stars near Sgr A* as a test of the quantum-modified metric. Our results indicate that quantum-modified metrics can produce measurable deviations in lensing observables, which may serve as targets for future precision tests of quantum gravity.