Black holes in 4D AdS Einstein Gauss Bonnet gravity with power: Yang Mills field

In this paper we construct an exact spherically symmetric black hole solution with a power Yang-Mills (YM) source in the context of 4D Einstein Gauss-Bonnet gravity (4D EGB). We choose our source as ((F mu nu F mu nu(a))-F-(a))q(F mu nu(a)F mu nu(a))q, where q is an arbitrary positive real number. Thereafter we study the horizon structure, thermodynamic issues like thermal stability and black hole phase transition. Our purpose here is to analyse the black hole space-time under the net effect coming from the Gauss-Bonnet coupling parameter alpha alpha and the nonlinear parameter q. We then evaluate all important thermodynamic quantities to establish the Smarr formula and the first law of thermodynamics in extended phase space. The behaviour of heat capacity as a function of horizon radius is thoroughly studied to understand the thermal stability of the black hole solution. An interesting phenomena of existence/absence of thermal phase transition occur due to the nonlinearity of YM source. For some values of the parameters, we find that the solution exhibits a first-order phase transition, like a van der Waals fluid. In addition, we also verify Maxwell's equal area law numerically by crucial analysis of Gibbs free energy as a function of temperature. Moreover, the critical exponents are derived and showed the universality class of the scaling behaviour of thermodynamic quantities near criticality.