Immirzi parameter and Noether charges in first order gravity

TL;DR

This paper extends Noether charge formulas in first order gravity with a negative cosmological constant, analyzing the role of topological invariants and the Immirzi parameter in black hole thermodynamics across various spacetime solutions.

Contribution

It generalizes Wald's approach to include topological terms and the Immirzi parameter in first order gravity, revealing their effects on black hole properties.

Findings

Immirzi parameter does not affect thermodynamics of AdS-Schwarzschild and AdS-Kerr black holes.

Topological black holes show no dependence on the Immirzi parameter.

AdS-Taub-NUT spacetime exhibits modifications in entropy and mass due to the Immirzi parameter.

Abstract

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