Surface charges toolkit for gravity

Frodden, Ernesto; Hidalgo, Diego

doi:10.1142/s0218271820500406

Cited by 20 publications

(21 citation statements)

References 76 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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“…that preserve its form. The corresponding conserved charges can then be computed using the known result for BF theory [58,59] δQ[λ bulk ] = − λ bulk , δB dτ E , (5.15)…”

Section: Jhep05(2021)162mentioning

confidence: 99%

Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

Gomis

Hidalgo

Salgado-Rebolledo

2021

J. High Energ. Phys.

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We construct the non-relativistic and Carrollian versions of Jackiw-Teitelboim gravity. In the second order formulation, there are no divergences in the non-relativistic and Carrollian limits. Instead, in the first order formalism, some divergences can be avoided by starting from a relativistic BF theory with (A)dS2 × ℝ gauge algebra. We show how to define the boundary duals of the gravity actions using the method of non-linear realisations and suitable Inverse Higgs constraints. In particular, the non-relativistic version of the Schwarzian action is constructed in this way. We derive the asymptotic symmetries of the theory, as well as the corresponding conserved charges and Newton-Cartan geometric structure. Finally, we show how the same construction applies to the Carrollian case.

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“…Conserved quantities in first order formulations of general relativity have recently been investigated from a variety of perspectives, see e.g. [8][9][10][11][12][13][14][15][16][17][18][19]. In the approach that we follow here [20][21][22], one constructs conserved co-dimension 2 forms in the linearized theory from the weakly vanishing Noether currents associated to gauge symmetries.…”

Section: Introductionmentioning

confidence: 99%

Conserved currents in the Palatini formulation of general relativity

Barnich¹,

Mao²,

Ruzziconi³

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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We derive the expressions for the local, on-shell closed co-dimension 2 forms in the Palatini formulation of general relativity and explicitly show their on-shell equivalence to those of the metric formulation. When compared to other first order formulations, two subtleties have to be addressed during the construction: off-shell non-metricity and the fact that the transformation of the connection under infinitesimal diffeomorphisms involves second order derivatives of the associated vector fields.

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Surface charges toolkit for gravity

Cited by 20 publications

References 76 publications

Null infinity as an open Hamiltonian system

Null infinity as an open Hamiltonian system

Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

Conserved currents in the Palatini formulation of general relativity

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