Black holes in (quartic) quasitopological gravity

Abstract

We construct quartic quasitopological gravity, a theory of gravity containing terms quartic in the curvature that yields second order differential equations in the spherically symmetric case. Up to a term proportional to the quartic term in Lovelock gravity we find a unique solution for this quartic case, valid in any dimensionality larger than 4 except 8. This case is the highest degree of curvature coupling for which explicit black hole solutions can be constructed, and we obtain and analyze the various black hole solutions that emerge from the field equations in (n + 1) dimensions.We discuss the thermodynamics of these black holes and compute their entropy as a function of the horizon radius. We then make some general remarks about K-th order quasitopological gravity, and point out that the basic structure of the solutions will be the same in any dimensionality for general K apart from particular cases. *

Quintic quasi-topological gravity

“…Quartic quasi-topological gravity is also argued to be unique in the original reference [14]. Whether or not the Quintic Quasi-topological theory here presented is unique, goes beyond the scope of this work and it would require at least to properly classify all the non-trivial, independent traces of the form T r (p) C 5 .…”

“…It's important to notice that Quartic Quasi-topological gravity in five dimensions does not belong to the family defined in equation (1.2), nevertheless on spherically symmetric spacetimes, the field equations are simple and reduce to a generalized Wheeler-like polynomial equation for the lapse function [15] (see also [16]). The authors of [14] also conjecture the existence of quasi-topological gravities of arbitrarily high degree in the curvature. The purpose of the present paper is to show that for Lagrangians that are quintic in the curvature, R 5 , this is indeed the case.…”

“…The mechanism that exorcizes the ghost on AdS in quasi-topological gravities is different. It was shown in [9] and [14] that around maximally symmetric backgrounds, cubic and quartic quasi-topological gravities lead to the same propagator than G.R. with an effective Newton's constant that depends on the values of the couplings.…”

“…It would be interesting to construct R 5 quasi-topological gravities in arbitrary dimensions. From what we have learned from the cubic [7] and quartic cases [14], it is natural to conjecture that this theory might exist for all dimensions lower than ten, and from dimension 11 it might reduce to Lovelock theory plus a combination of invariants whose contribution cancels when evaluated on spherically symmetric spacetimes.…”

“…Motivated by broadening the family of four-dimensional CFTs with relatively simple gravity duals, in reference [14] the authors successfully look for a quartic theory with second order field equations on spherical symmetry. Such theory was dubbed Quartic Quasi-topological gravity and when supplemented with terms of lower order in the Riemann tensor, leads to second order linearized field equations around AdS spacetime.…”