Perturbations and modified hawking radiation in cylindrical black holes within f<i> (R)</i> and Ricci-Inverse gravity theories

This paper investigates scalar and vector perturbations of cylindrical black holes within the frameworks of f(R)-gravity and Ricci-Inverse (RI) gravity theories. We begin by explicitly writing the massless Klein{Gordon equation and deriving an effective potential for scalar perturbations. For vector perturbations, we apply Maxwell's equation to obtain an expression for the vector perturbation potential. In both cases, we consider black holes as background solutions within the aforementioned gravity theories. Next, we explore the modified Hawking radiation in these black hole solutions, analyzing the impact of coupling constants. Additionally, we examine the thermodynamic properties of black holes using the Generalized Uncertainty Principle (GUP), which introduces quantum corrections to Hawking radiation. We derive the GUP-modified Hawking temperature and entropy, revealing notable deviations from classical results and emphasizing the quantum gravitational effects present in these extended frameworks.