Configuration entropy and thermodynamics phase transition of black hole in f(R) gravity

Abstract

Starting from a d$-$dimensional black hole (BH) in $f\left(R\right)$ gravity, we analyzed the effect of modified gravity on critical point parameters, the difference in number densities, and configuration entropy during the BH phase transition phenomenon. From our investigations, consistent results with charged AdS BH are obtained that is holographic dual of van der Waal’s fluid and hence the BH in modified gravity. The thermodynamic pressure, temperature, and free energy are affected by $f\left(R\right)$ gravity. The difference in the number densities of molecules (small and large BHs) and configuration entropy are investigated as a function of reduced temperature $\left(\tilde{\tau }\right)$. The difference in the number densities of BH molecules in $f\left(R\right)$ gravity decreases with the increase in $\tilde{\tau }$, whereas, $S_{con}$ increases monotonically and becomes a concave function with the increase in space–time dimensions. The relation between the difference in the number density of BH molecules and space–time dimensions $\left(d\right)$ decreases with the increase in dimension $d$. Finally, using our results, the laws of BH Physics are also discussed.