Entropy in Poincar\'e gauge theory: Hamiltonian approach

The canonical generator $G$ of local symmetries in Poincar'e gauge theory is constructed as an integral over a spatial section $\mathrm{\Sigma }$ of spacetime. Its regularity (differentiability) on the phase space is ensured by adding a suitable surface term, an integral over the boundary of $\mathrm{\Sigma }$ at infinity, which represents the asymptotic canonical charge. For black hole solutions, $\mathrm{\Sigma }$ has two boundaries, one at infinity and the other at horizon. It is shown that the canonical charge at horizon defines entropy, whereas the regularity of $G$ implies the first law of black hole thermodynamics.