Immirzi parameter and Noether charges in first order gravity

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.

Magnetic mass in 4D AdS gravity

“…[35,36] in first-order formalism. In this Riemann-Cartan approach, the parity-violating sector appears enlarged by the Holst and Nieh-Yang terms, which are identically vanishing in Riemannian gravity [37].…”

Higher derivative asymptotic charges and internal Lorentz symmetries

“…which can be expanded in orders of 1/r, with [3] To reiterate, the criterion for fixing Λ ab in the asymptotic case is very different to that used in the global case. In the former case, the criterion is that once a vierbein has been 6 To be clear, δ ξ E i I represents an explicit transformation of the metric component functions that appear in E i I using the prescription derived from δ ξ gµν = L ξ gµν . In particular, δ ξ Êi I = 0.…”

“…[3], it was shown that asymptotic BMS charges derived from such terms would be subleading at null infinity. Higher derivative terms have been considered in various settings in the literature [4][5][6][7][8][9][10][11]. While the importance of higher derivative terms has been stressed in much of the literature connected to the Anti-de Sitter case starting with Ref.…”

Manifold invariants affect dynamics in anti de Sitter gravity

“…R − and Barbero-Immirzi parameter γ ∈ R \ {0} on a four-dimensional manifold (M, e, A) with generic boundary ∂M is [1][2][3][4]:…”

“…g ab = η IJ e I a ⊗ e J b and Ω I J = dA I J + A I K ∧ A K J = (1/2)R I JKL e K ∧ e L , with R I JKL being the Riemann tensor. The first-order Holst action with negative cosmological constant Λ := −3ℓ −2 ∈ R − and Barbero-Immirzi parameter γ ∈ R \ {0} on a four-dimensional manifold (M, e, A) with generic boundary ∂M is [1][2][3][4]:…”