Quartic Quasi-topological Gravity, Black Holes and Holography

Abstract: In this paper, we derive the field equations of quartic quasi-topological gravity by varying the action with respect to the metric. Also, we obtain the linearized graviton equations in the AdS background and find that it is governed by a second-order field equation as in the cases of Einstein, Lovelock or cubic quasi-topological gravities. But in contrast to the cubic quasi-topological gravity, the linearized field equation around a black hole has fourth-order radial derivative of the perturbation. Moreover, we analyze the conditions of having ghost free AdS solutions and AdS planar black holes. In addition, we compute the central charges of the dual conformal field theory of this gravity theory by studying holographic Weyl anomaly. Finally, we consider the effect of quartic term on the causality of dual theory in the tensor channel and show that, in the contrast to the trivial result of cubic quasi-topological gravity, the existence of both cubic and quartic terms leads to a non-trivial constraint. However, this constraint does not imply any lower positive bound on the viscosity/entropy ratio.