First-Order GUP Corrections of Black Hole Thermodynamics in the Framework of f ( R ) $f(R)$ Gravity

The black hole geometry in the $f\left(R\right)$ gravity theory is studied in this paper, which incorporates the cosmological constant and charge field. The tunnelling radiation of black holes and their corrections by applying the generalized uncertainty principle (GUP) are studied. In the GUP framework, the modified field and Wentzel–Kramers–Brillouin (WKB) approximation are studied. Using a semi-classical approach, the imaginary particle action along the vector charge field is calculated. It is shown that quantum gravity has a more significant influence on the tunnelling radiation. In the different cases of cosmic constant value, it is investigated that the corrected Hawking temperature is substantial for an $f\left(R\right)$ model in the context of GUP to study the equilibrium states of black holes. Further, the reliability of the fundamental principle of thermodynamics to describe this scenario under the condition of the GUP frame is analyzed, which is the corrected temperature and entropy of the $f\left(R\right)$ theory for black hole geometry.