Yang–Mills black holes in quasitopological gravity

In this paper, we formulate two new classes of black hole solutions in higher curvature quartic quasitopological gravity with nonabelian Yang–Mills theory. At first step, we consider the SO(n) and SO(n-1,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SO(n-1,1)$$\end{document} semisimple gauge groups. We obtain the analytic quartic quasitopological Yang–Mills black hole solutions. Real solutions are only accessible for the positive value of the redefined quartic quasitopological gravity coefficient, μ4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _{4}$$\end{document}. These solutions have a finite value and an essential singularity at the origin, r=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=0$$\end{document} for space dimension higher than 8. We also probe the thermodynamic and critical behavior of the quasitopological Yang–Mills black hole. The obtained solutions may be thermally stable only in the canonical ensemble. They may also show a first order phase transition from a small to a large black hole. In the second step, we obtain the pure quasitopological Yang–Mills black hole solutions. For the positive cosmological constant and the space dimensions greater than eight, the pure quasitopological Yang–Mills solutions have the ability to produce both the asymptotically AdS and dS black holes for respectively the negative and positive constant curvatures, k=-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=-1$$\end{document} and k=+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=+1$$\end{document}. This is unlike the quasitopological Yang–Mills theory which can lead to just the asymptotically dS solutions for Λ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda >0$$\end{document}. The pure quasitopological Yang–Mills black hole is not thermally stable.