Boundary conditions in first order gravity: Hamiltonian and Ensemble

TL;DR

This paper explores two boundary conditions in first order gravity with different cosmological constants, demonstrating their compatibility with black hole thermodynamics and canonical ensembles, and deriving a quasilocal energy in one case.

Contribution

It introduces and compares two boundary conditions in first order gravity, establishing their thermodynamic and energetic properties.

Findings

Both boundary conditions reproduce standard black hole thermodynamics.

Each boundary condition defines a valid canonical ensemble.

A quasilocal energy is derived for the null cosmological constant case.

Abstract

In this work two different boundary conditions for first order gravity, corresponding to a null and a negative cosmological constant respectively, are studied. Both boundary conditions allows to obtain the standard black hole thermodynamics. Furthermore both boundary conditions define a canonical ensemble. Additionally the quasilocal energy definition is obtained for the null cosmological constant case.