The Hamilton-Jacobi analysis for higher-order Chern-Simons gravity

TL;DR

This paper applies Hamilton-Jacobi analysis to higher-order Chern-Simons gravity, identifying Hamiltonians, constructing differential equations, and exploring symmetries, providing a comprehensive approach compared to existing methods.

Contribution

It introduces a Hamilton-Jacobi framework for higher-order Chern-Simons gravity, detailing Hamiltonians, differential equations, and symmetry analysis, enhancing understanding of the theory's structure.

Findings

Complete set of Hamiltonians identified

Fundamental Hamilton-Jacobi differential constructed

Symmetries of the theory analyzed

Abstract

The Hamilton-Jacobi [$HJ$] analysis for higher-order Chern-Simons gravity is performed. The complete set of $HJ$ Hamiltonians are identified and a fundamental $HJ$ differential is constructed, from which the characteristic equations are obtained. In addition, the symmetries of the theory are identified and the obtained results are compared with other approaches reported in the literature.