Advanced Lectures on General Relativity

Compère, Geoffrey; Fiorucci, Adrien

doi:10.48550/arxiv.1801.07064

Cited by 52 publications

(81 citation statements)

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“…This is just Gauss's theorem, which we can see is given by a special case of Noether's 1.5th theorem. 3 The fact that empty gauge transformations give vanishing currents and divergence-free surface charges is called the "Generalized Noether theorem" in the literature [32,33].…”

Section: Gauge Symmetry and Noether's 15th Theoremmentioning

confidence: 99%

“…This was done, for instance, in Wald's classic paper [30] where he gave a Noetherian proof of the first law of black hole thermodynamics. However, the most general "best" proscription for defining these surface charges is still a matter of debate, with different approaches used by different practitioners in different contexts [32,[54][55][56][57]. Now, the above equation does not specify a unique solution for G(k) due to the fact that one cannot divide by k 2 when it is 0.…”

Section: B3 Noether's 15th Theoremmentioning

confidence: 99%

“…One must in general determine what the "best" boundary term to add is. In EM we can just use the naive Θ µ , but in GR there are multiple options which have different properties[32].…”

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confidence: 99%

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From Noether's Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems

Miller¹

2021

Preprint

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Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the conservation of soft charge constrains the overall amount of radiation emitted per angle. Here we describe the physical consequences of soft charge conservation and give fresh accounts of the roles of spacelike and timelike infinity in these conservation laws. We conclude by exploring the possibility of creating a dual boundary theory of electromagnetism.

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Section: Gauge Symmetry and Noether's 15th Theoremmentioning

confidence: 99%

Section: B3 Noether's 15th Theoremmentioning

confidence: 99%

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From Noether's Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems

Miller¹

2021

Preprint

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“…For a detailed discussion of this formalism, we refer the reader to[27,28,29]. This was first analyzed near null infinity in[4,3] 15.…”

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confidence: 99%

“…Charges corresponding to gauge symmetries require a study of the generalized Noether theorem, which is reviewed in[27] 19. For a computation of the charge in QED, refer to appendix D.3 and also[32,33].…”

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The Asymptotic Structure of Gravity in Higher Even Dimensions

Chowdhury¹,

Mishra²,

Prabhu³

2022

Preprint

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We investigate the notion of asymptotic symmetries in classical gravity in higher even dimensions, with D = 6 space-time dimensions as the prototype. Unlike in four dimensions, certain non-linearities persist which necessitates the complete non-linear analysis we undertake. We show that the free data is parametrized by a pair of symmetric trace-free tensors at future (past) null infinity. This involves a redefinition of the radiative field. We define a symplectic structure generating the radiative phase space at I ± with appropriate boundary conditions which are preserved by the action of supertranslations. We derive the charge associated with super-translation vector fields and show that it matches with the charge derived using the equations of motion in the full non-linear theory. We elaborate on the precise relationship between the super-translation charge, soft theorem and the "gravitational memory" in six space-time dimensions, thus providing the first example of an infrared triangle in non-linear gravity beyond four dimensions.

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Subleading BMS charges and fake news near null infinity

Godazgar

Pope

2019

J. High Energ. Phys.

112

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In this paper we establish a relation between the non-linearly conserved Newman-Penrose charges and certain subleading terms in a large-r expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a 1/r-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. 1/r 0 , one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. At subleading orders, analogous terms in general provide obstructions to the integrability of the corresponding charges. Since the subleading terms are defined close to null infinity, but vanish actually at infinity, the analogous obstructions are not associated with genuine Bondi news. One may instead describe them as corresponding to "fake news." At order r −3 , we find that a set of integrable charges can be defined and that these are related to the ten non-linearly conserved Newman-Penrose charges.

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Advanced Lectures on General Relativity

Cited by 52 publications

References 0 publications

From Noether's Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems

From Noether's Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems

The Asymptotic Structure of Gravity in Higher Even Dimensions

Subleading BMS charges and fake news near null infinity

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