Geometrodynamics of spherically symmetric Lovelock gravity

Abstract

We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kucha\v{r} in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner-Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher-dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mechanics, Hamiltonian thermodynamics and formation of generic Lovelock black holes.