Lovelock black holes dressed with a conformally coupled scalar field and nonlinear Yang–Mills charge

In this work, we derive the new hairy black hole solutions of the Lovelock-scalar gravity sourced by three different models of the nonlinear Yang–Mills field. First, we derive the Lovelock polynomial that deduces the nonlinear Yang–Mills black hole solution in a general Lovelock-scalar theory of gravity. Next, we determine the solutions that describe these objects in the context of Gauss–Bonnet-scalar and third order Lovelock-scalar theories. In addition, we examine the physical characteristics and the impact of nonlinear Yang–Mills field and scalar hair on the thermodynamic stability of resultant gravitating objects.