Lovelock black holes with nonmaximally symmetric horizons

Abstract

We present a new class of black hole solutions in third-order Lovelock gravity whose horizons are Einstein space with two supplementary conditions on their Weyl tensors. These solutions are obtained with the advantage of higher curvature terms appearing in Lovelock gravity. We find that while the solution of third-order Lovelock gravity with constant-curvature horizon in the absence of a mass parameter is the anti de Sitter (AdS) metric, this kind of solution with nonconstant- curvature horizon is only asymptotically AdS and may have horizon. We also find that one may have an extreme black hole with non-constant curvature horizon whose Ricci scalar is zero or a positive constant, while there is no such black hole with constant-curvature horizon. Furthermore, the thermodynamics of the black holes in the two cases of constant- and nonconstant-curvature horizons are different drastically. Specially, we consider the thermodynamics of black holes with vanishing Ricci scalar and find that in contrast to the case of black holes of Lovelock gravity with constant-curvature horizon, the area law of entropy is not satisfied. Finally, we investigate the stability of these black holes both locally and globally and find that while the black holes with constant curvature horizons are stable both locally and globally, those with nonconstant-curvature horizons have unstable phases.