The Hamilton-Jacobi analysis for higher-order modified gravity

TL;DR

This paper applies Hamilton-Jacobi analysis to a higher-order modified gravity theory, specifically Chern-Simons gravity, revealing its Hamiltonian structure, symmetries, and stability properties.

Contribution

It provides a detailed Hamilton-Jacobi framework for Chern-Simons modified gravity, including Hamiltonian structure, symmetry analysis, and stability considerations.

Findings

Hamiltonian structure of Chern-Simons gravity is fully characterized

Symmetries of the theory are identified

An Ostrogradsky instability is addressed and removed

Abstract

The Hamilton-Jacobi $[HJ]$ study for the Chern-Simons $[CS]$ modification of general relativity $[GR]$ is performed. The complete structure of the Hamiltonians and the generalized brackets are reported, from these results the $HJ$ fundamental differential is constructed and the symmetries of the theory are found. By using the Hamiltonians we remove an apparent Ostrogradsky's instability and the new structure of the hamiltonian is reported. In addition, the counting of physical degrees of freedom is developed and some remarks are discussed.