Exotic black hole thermodynamics in third-order Lovelock gravity

The generalisation of Birkhoff’s theorem to higher dimensions in Lovelock gravity allows for black hole solutions with horizon geometries of non-constant curvature. We investigate thermodynamic aspects of these ‘exotic’ black hole solutions, with a particular emphasis on their phase transitions. We consider an extended phase space where the cosmological constant acts as a thermodynamic pressure, and examine both uncharged and U(1) charged solutions. In d = 7, black hole solutions are restricted to having constant curvature horizon base manifolds. Uncharged d = 7 black holes possess novel triple point phenomena analogous to those recently uncovered in exotic d = 6 black holes in Gauss-Bonnet gravity, while their charged counterparts generically undergo small-large black hole phase transitions. In d = 8, we find that both charged and uncharged black holes exhibit triple point behaviour and small-large black hole transitions. We also show that a wide range of ‘exotic’ horizon geometries can be ruled out due to the appearance of naked singularities.