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The framework of SO(3,2) constrained BF theory applied to gravity makes itpossible to generalize formulas for gravitational diffeomorphic Noether charges(mass, angular momentum, and entropy). It extends Wald's approach to the caseof first order gravity with a negative cosmological constant, the Holstmodification and the topological terms (Nieh-Yan, Euler, and Pontryagin).Topological invariants play essential role contributing to the boundary termsin the regularization scheme for the asymptotically AdS spacetimes, so that thedifferentiability of the action is automatically secured. Intriguingly, itturns out that the black hole thermodynamics does not depend on the Immirziparameter for the AdS-Schwarzschild, AdS-Kerr, and topological black holes,whereas a nontrivial modification appears for the AdS-Taub-NUT spacetime, whereit impacts not only the entropy, but also the total mass.

Immirzi parameter and Noether charges in first order gravity