f(Lovelock) theories of gravity

TL;DR

f(Lovelock) theories extend traditional gravity models by depending on functions of Euler densities, offering ghost-free, scalar-tensor equivalences, and novel black hole solutions with potential holographic applications.

Contribution

This paper introduces the study of f(Lovelock) gravities, identifying boundary terms, scalar-tensor equivalences, and analyzing linearized equations and black hole solutions in various dimensions.

Findings

No ghost-like massive gravitons propagate on maximally symmetric backgrounds.

Certain models have only the usual graviton as the dynamical field, similar to Einstein gravity.

Constructed new asymptotically flat and AdS/dS black hole solutions.

Abstract

f(Lovelock) gravities are simple generalizations of the usual f(R) and Lovelock theories in which the gravitational action depends on some arbitrary function of the corresponding dimensionally-extended Euler densities. In this paper we study several aspects of these theories in general dimensions. We start by identifying the generalized boundary term which makes the gravitational variational problem well-posed. Then, we show that these theories are equivalent to certain scalar-tensor theories and how this relation is characterized by the Hessian of f. We also study the linearized equations of the theory on general maximally symmetric backgrounds. Remarkably, we find that these theories do not propagate the usual ghost-like massive gravitons characteristic of higher-derivative gravities on such backgrounds. In some non-trivial cases, the additional scalar associated to the trace of the metric perturbation is also absent, being the usual graviton the only dynamical field. In those cases, the linearized equations are exactly the same as in Einstein gravity up to an overall factor, making them appealing as holographic toy models. We also find constraints on the couplings of a broad family of five-dimensional f(Lovelock) theories using holographic entanglement entropy. Finally, we construct new analytic asymptotically flat and AdS/dS black hole solutions for some classes of f(Lovelock) gravities in various dimensions.