Asymptotic symmetries from finite boxes

It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite sys...

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Bibliographic Details
Published in:Classical and quantum gravity 2016-01, Vol.33 (1), p.15013-15024
Main Authors: Andrade, Tomás, Marolf, Donald
Format: Article
Language:English
Subjects:
Algebra
Asymptotic properties
asymptotic symmetries
Boundary conditions
Dirichlet boundary conditions
Dirichlet problem
Flats
Gravitation
gravity
Mathematical analysis
Symmetry
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Summary:It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/33/1/015013