Geometrodynamics of spherically symmetric Lovelock gravity

TL;DR

This paper derives the Hamiltonian formulation for spherically symmetric Lovelock gravity, showing it parallels general relativity and paving the way for quantum and thermodynamic studies of Lovelock black holes.

Contribution

It extends the geometrodynamics approach to Lovelock gravity, revealing a simple Hamiltonian form similar to general relativity, facilitating future quantum and thermodynamic analyses.

Findings

Hamiltonian for Lovelock gravity mirrors that of general relativity.

Supports Lovelock gravity as a natural higher-dimensional extension.

Enables future studies of quantum mechanics and thermodynamics of Lovelock black holes.

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.