# Entropy in Poincar\'e gauge theory: Hamiltonian approach

## TL;DR

This paper develops a Hamiltonian framework for Poincaré gauge theory, linking boundary terms to black hole entropy and thermodynamics, thus providing a deeper understanding of gravitational entropy in gauge theories.

## Contribution

It constructs the canonical generator for local symmetries in Poincaré gauge theory and relates boundary terms to black hole entropy and thermodynamic laws.

## Key findings

- Canonical charge at horizon defines black hole entropy.
- Regularity of the generator implies the first law of thermodynamics.
- Boundary terms encode asymptotic charges and thermodynamic properties.

## Abstract

The canonical generator $G$ of local symmetries in Poincar\'e gauge theory is constructed as an integral over a spatial section $\Sigma$ of spacetime. Its regularity (differentiability) on the phase space is ensured by adding a suitable surface term, an integral over the boundary of $\Sigma$ at infinity, which represents the asymptotic canonical charge. For black hole solutions, $\Sigma$ 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.