Hamilton–Jacobi analysis of the Freidel–Starodubtsev BF (A)dS gravity action

Abstract

In this work, we perform the Hamilton–Jacobi analysis of a modified gravity action, the so-called Freidel–Starodubtsev model. The complete set of involutive Hamiltonians that guarantee the system’s integrability is obtained. The generalized Poisson brackets are calculated in the metric phase by means of a suitable constraint matrix inversion. We also present a discussion about the metric and non-metric degrees of freedom. From the fundamental differential we recover the equations of motion and explicitly obtain the generators of local Lorentz transformations and also diffeomorphisms for the tetrad and the spin connection fields.