A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function

We present a new cubic theory of gravity in five dimensions which has second order traced field equations, analogous to BHT new massive gravity in three dimensions. Moreover, for static spherically symmetric spacetimes all the field equations are of second order, and the theory admits a new asymptotically locally flat black hole. Furthermore, we prove the uniqueness of this solution, study its thermodynamical properties, and show the existence of a C-function for the theory following the arguments of Anber and Kastor (arXiv:0802.1290 [hep-th]) in pure Lovelock theories. Finally, we include the Einstein-Gauss-Bonnet and cosmological terms and we find new asymptotically AdS black holes at the point where the three maximally symmetric solutions of the theory coincide. These black holes may also possess a Cauchy horizon.Comment: 21 pages, no figures, V2: two appendices and some references added, V3: New section on the generalization to arbitrary higher order. Analogy with BHT new massive gravity Lagrangian made more precise, V4: Typos corrected. To appear in CQ