Extensions of the asymptotic symmetry algebra of general relativity

A bstract We consider a recently proposed extension of the Bondi-Metzner-Sachs algebra to include arbitrary infinitesimal diffeomorphisms on a 2-sphere. To realize this extended algebra as asymptotic symmetries, we work with an extended class of spacetimes in which the unphysical metric at null infi...

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Published inThe journal of high energy physics Vol. 2020; no. 1; pp. 1 - 27
Main Authors Flanagan, Éanna É., Prabhu, Kartik, Shehzad, Ibrahim
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020
Springer Nature B.V
SpringerOpen
Subjects
Algebra
Asymptotic properties
Classical and Quantum Gravitation
Classical Theories of Gravity
Divergence
Elementary Particles
Gauge Symmetry
High energy physics
Infinity
Isomorphism
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity
Relativity Theory
Space-Time Symmetries
String Theory
Symmetry
Theory of relativity
Translations
Gauge Symmetry
Classical Theories of Gravity
Space-Time Symmetries
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Summary:A bstract We consider a recently proposed extension of the Bondi-Metzner-Sachs algebra to include arbitrary infinitesimal diffeomorphisms on a 2-sphere. To realize this extended algebra as asymptotic symmetries, we work with an extended class of spacetimes in which the unphysical metric at null infinity is not universal. We show that the symplectic current evaluated on these extended symmetries is divergent in the limit to null infinity. We also show that this divergence cannot be removed by a local and covariant redefinition of the symplectic current. This suggests that such an extended symmetry algebra cannot be realized as symmetries on the phase space of vacuum general relativity at null infinity, and that the corresponding asymptotic charges are ill-defined. However, a possible loophole in the argument is the possibility that symplectic current may not need to be covariant in order to have a covariant symplectic form. We also show that the extended algebra does not have a preferred subalgebra of translations and therefore does not admit a universal definition of Bondi 4-momentum.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2020)002