Gielen, S. orcid.org/0000-0002-8653-5430 and Wise, D.K. (2012) Linking covariant and canonical general relativity via local observers. General Relativity and Gravitation, 44 (12). pp. 3103-3109. ISSN 0001-7701
Abstract
Hamiltonian gravity, relying on arbitrary choices of ‘space,’ can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between ‘spatial’ and ‘temporal’ variables. The key is viewing dynamical fields from the perspective of a field of observers—a unit timelike vector field that also transforms under local Lorentz transformations. On one hand, all fields are spacetime fields, covariant under spacetime symmeties. On the other, when the observer field is normal to a spatial foliation, the fields automatically fall into Hamiltonian form, recovering the Ashtekar formulation. We argue this provides a bridge between Ashtekar variables and covariant phase space methods. We also outline a framework where the ‘space of observers’ is fundamental, and spacetime geometry itself may be observer-dependent.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2012 Springer. This is an author-produced version of a paper subsequently published in General Relativity and Gravitation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Lorentz covariance; Lorentz symmetry breaking; Covariant real Ashtekar variables; Observer space; Relative locality |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Oct 2019 13:45 |
Last Modified: | 08 Oct 2019 14:27 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s10714-012-1443-3 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:151743 |