Concise symplectic formulation for tetrad gravity

Díaz, Bogar; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.

doi:10.1103/physrevd.103.024051

Cited by 11 publications

(9 citation statements)

References 15 publications

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“…Therefore, we had to impose a weaker condition, namely (5.14), which can always be reached thanks to the gauge freedom m a → e i ϕ m a . Our discussion completes earlier results [52][53][54][55][56][57][58][59] on the subject by clarifying the falloff conditions on the covariant phase space in terms of an adapted Newman-Penrose null tetrad on a generic double null foliation of spacetime.…”

Section: Jhep04(2021)095supporting

confidence: 81%

Null infinity as an open Hamiltonian system

Wieland

2021

J. High Energ. Phys.

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When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time-dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent Hamiltonian on the covariant phase space. Our derivation starts from the Hamiltonian formulation in domains with boundaries that are null. We introduce the most general boundary conditions on a generic such null boundary, and compute quasi-local charges for boosts, energy and angular momentum. Initially, these domains are at finite distance, such that there is a natural IR regulator. To remove the IR regulator, we introduce a double null foliation together with an adapted Newman-Penrose null tetrad. Both null directions are surface orthogonal. We study the falloff conditions for such specific null foliations and take the limit to null infinity. At null infinity, we recover the Bondi mass and the usual covariant phase space for the two radiative modes at the full non-perturbative level. Apart from technical results, the framework gives two important physical insights. First of all, it explains the physical significance of the corner term that is added in the Wald-Zoupas framework to render the quasi-conserved charges integrable. The term to be added is simply the derivative of the Hamiltonian with respect to the background fields that drive the time-dependence of the Hamiltonian. Secondly, we propose a new interpretation of the Bondi mass as the thermodynamical free energy of gravitational edge modes at future null infinity. The Bondi mass law is then simply the statement that the free energy always decreases on its way towards thermal equilibrium.

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Section: Jhep04(2021)095supporting

confidence: 81%

Null infinity as an open Hamiltonian system

Wieland

2021

J. High Energ. Phys.

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“…First, tetrads provide a natural way to incorporate fermion fields into the theory. Second, the tetrad formalism leads naturally to the Ashtekar formulation, one of the main avenues for the quantization of gravity [4,5]. Finally, local Lorentz gauge invariance plays a crucial role in this formalism and it may introduce significant differences in the treatment of the theory compared with the metric formulation.…”

Section: Introductionmentioning

confidence: 99%

Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

Margalef-Bentabol

Varo²,

Villaseñor³

2021

Phys. Rev. D

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We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this end, we will rely on the cohomological approach provided by the relative bicomplex framework. Finally, we discuss some of the physical implications derived from this equivalence in the context of singularity identification through curvature invariants.

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“…The hope -ultimately realized-is that the analysis will provide an interesting perspective on the Hamiltonian formulation of unimodular gravity. As we will see, the final description given by the GNH approach -one of the results of the present paper-is concise and clean (see [14] for a short partial summary involving just the Holst action). It naturally leads to the real Ashtekar formulation of general relativity and illuminates some issues related to the role of the time gauge and the Immirzi parameter, both at the classical and quantum level [14].…”

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confidence: 66%

“…However, in the present example, it is easier to break the objects with the fixed foliation using ∂ τ . Besides, in this case, the comparison with the unparametrized version is straightforward [14]. Obviously, ı ∂τ α t = 0 and ı ∂τ α = 0.…”

Section: Lagrangian Formulationmentioning

confidence: 95%

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Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

2021

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We give a detailed account of the Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper.

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Concise symplectic formulation for tetrad gravity

Abstract: We discuss a simple symplectic formulation for tetrad gravity that leads to the real Ashtekar variables in a direct and transparent way. It also sheds light on the role of the Immirzi parameter and the time gauge.

Cited by 11 publications

References 15 publications

Null infinity as an open Hamiltonian system

Null infinity as an open Hamiltonian system

Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

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