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

TL;DR

The paper introduces a novel cubic curvature invariant in five dimensions with a second-order-trace property, mirroring features of BHT gravity in 3D. It demonstrates that static spherically symmetric solutions evade higher-derivative pathologies, yielding a unique asymptotically locally flat black hole and a Birkhoff-type theorem. The authors construct a Wald-type C-function and show its monotonicity under energy conditions, linking it to black hole entropy, and they explore thermodynamics, stability, and AdS extensions, including a special point with coincident vacua that admits asymptotically AdS black holes. They then outline a systematic generalization to arbitrary higher-order invariants, providing explicit k-th order results in seven dimensions and discussing the role of Weyl invariants. Overall, the work connects higher-curvature gravity in higher dimensions with Lovelock-like behavior, Birkhoff's theorem, holographic C-functions, and a framework for extending to higher orders.

Abstract

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.