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

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.