Hamiltonian Structure of Poincaré Gauge Theory and Separation of Non-Dynamical Variables in Exact Torsion Solutions

Abstract

The canonical Hamiltonian of the Poincaré gauge theory of gravity is reanalyzed for generic Lagrangians. It is shown that the time components e0α and Γ0αβ of the tetrad and the linear connection fields of a Riemann-Cartan space-time U4 constitute gauge degrees of freedom which remain non-dynamical during the time evolution of the system. Whereas the e0α are to be identified with the lapse and shift functions Nα known from the ADM formalism in Einstein's theory, the additional Lorentz degrces of freedom Γ0αβ are pertinent to Poincaré gauge models. These non-dynamical variables are instrumental in the derivation of exact torsion solutions obeying modified double duality conditions for the U4-curvature. Thereby, in the case of spherical symmetry and for the charged Taub-NUT metric, we obtain the most general torsion configuration for a large class of quadratic Lagrangians. Previously found solutions are contained therein and can be recovered after fixing special “gauge”.