On the Hamiltonian Analysis of Spin-3 Chern-Simons-Like Theories of Gravity

TL;DR

This paper develops a Hamiltonian framework for spin-3 Chern-Simons-like gravity theories in (2+1) dimensions to determine their local degrees of freedom, applying it to specific models and revealing their dynamical properties.

Contribution

It introduces a Hamiltonian analysis method for spin-3 Chern-Simons-like gravity theories and applies it to identify their local degrees of freedom.

Findings

Spin-3 Einstein-Cartan gravity has zero local degrees of freedom.

Spin-3 topologically massive gravity has one local degree of freedom.

The Hamiltonian formulation effectively determines the dynamical content of these theories.

Abstract

In this paper, we consider spin-3 Chern-Simons-like theories of gravity as extended theories of spin-3 gravity in (2+1)- dimension. In order to determine the number of local degrees of freedom we present the Hamiltonian formulation of these theories. We extract the Hamiltonian density, then we find primary and secondary constraints of these theories. Then we obtain the Poisson brackets of the primary and the secondary constraints. After that we count the number of local degrees of freedom of spin-3 Chern-Simons-like theories of gravity. We apply this method on spin-3 Einstein-Cartan gravity and spin-3 topologically massive gravity. According to the our results the spin-3 Einstein-Cartan gravity and the spin-3 topologically massive gravity have respectively zero and one bulk local degree of freedom.