On the maximally symmetric vacua of generic Lovelock gravities

TL;DR

This paper surveys Lovelock gravity's maximally symmetric vacua, their polynomial characterization, black hole solutions, linearization around vacua, and conserved charge computations, highlighting the structure and special vacua of the theory.

Contribution

It provides a comprehensive analysis of Lovelock gravity vacua, including polynomial root characterization, black hole solutions, linearization methods, and conserved charge calculations.

Findings

Vacua determined by roots of a dimension-dependent polynomial.

Black hole solutions derived using symmetric criticality principle.

Method for computing conserved charges in Lovelock gravity.

Abstract

We survey elementary features of Lovelock gravity and its maximally symmetric vacuum solutions. The latter is solely determined by the real roots of a dimension-dependent polynomial. We also recover the static spherically symmetric (black hole) solutions of Lovelock gravity using Palais' symmetric criticality principle. We show how to linearize the generic field equations of Lovelock models about a given maximally symmetric vacuum, which turns out to factorize into the product of yet another dimension-dependent polynomial and the linearized Einstein tensor about the relevant background. We also describe how to compute conserved charges using linearized field equations along with the relevant background Killing isometries. We further describe and discuss the special vacua which are defined by the simultaneous vanishing of the aforementioned polynomials.