Refined form of the paper "Canonical formalism of the f(R)-type gravity in terms of Lie derivatives"

TL;DR

This paper refines a canonical formalism for f(R)-type gravity by extensively using Lie derivatives to avoid time derivatives, improving the mathematical framework of the theory.

Contribution

It introduces a more comprehensive use of Lie derivatives in the canonical formalism of f(R) gravity, removing reliance on time derivatives.

Findings

Enhanced formalism with Lie derivatives

Elimination of time derivatives in the framework

Improved mathematical consistency

Abstract

We refine the presentation of the previous paper of our group, Y.Ezawa et al., Class. Quantum Grav. {\bf 23} (2006), 3205 [arXiv:gr-qc/0507060]. In that paper, we proposed a canonical formalism of f(R)-type generalized gravity by using the Lie derivatives instead of the time derivatives. However, the use of the Lie derivatives was not sufficient. In this note, we make use of the Lie derivatives as far as possible, so that no time derivatives are used.