Spinning higher dimensional black hole solutions in f(R) gravity coupled with non-linear Yang–Mills field and P-V criticality

Abstract

We construct a higher-dimensional spinning solution in f(R) gravity coupled with non-linear Yang–Mills(YM) field via complex transformations which is known as Newman–Janis Algorithm(NJA). This task shows that the NJA can be applied in higher dimensional geometry as well. In analyzing the horizon properties, we have shown that the event horizon is not a constant parameter and it is related to the angular part of the metric (θ1). From analyzing the local stability near the origin, we have shown that the solutions are more stable if the rotation parameter(a) increases. Motivated by the thermodynamical analogy of black holes and Van der Waals liquid/gas systems, in this work, we investigate P–V criticality of both non-rotating and rotating black hole solutions in f(R) gravity coupled with non-linear Yang–Mills field. We extend the phase space by considering the cosmological constant as thermodynamic pressure. We obtain critical values of the thermodynamic coordinates and plot the relevant P–V diagrams.