Gielen, S. orcid.org/0000-0002-8653-5430 (2013) Contracted Lorentz invariance for gravity with a preferred foliation. Physical Review D, 88 (6). ISSN 2470-0010
Abstract
In canonical gravity, the choice of a local time direction is not obviously compatible with local Lorentz invariance. One way to address this issue is to view gravity as a gauge theory on observer space, rather than spacetime. In a Lorentz covariant theory, observer space is the space of unit future-directed timelike vectors; picking such a vector locally breaks the symmetry to a subgroup SO(D) of SO(D,1), so that on observer space the local symmetry group is SO(D). Observer space geometries naturally describe any gravitational theory that only assumes local invariance under SO(D). Here we construct nonrelativistic observer spaces for gravity with a fixed foliation, applicable to preferred foliation theories such as Hořava–Lifshitz gravity. Different Hořava–Lifshitz observers at a point are related by a change in the shift vector, leaving the preferred foliation invariant. Gravity is formulated on a nonrelativistic frame bundle with structure group ISO(D); the shift vector acts as a symmetry breaking field breaking ISO(D) symmetry spontaneously to SO(D). A natural torsion-free connection is constructed, including the usual SO(D,1) connection of relativistic gravity plus terms depending on derivatives of the shift vector. This observer space geometry provides a novel geometric framework for the study of preferred foliation theories.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013 American Physical Society. This is an author-produced version of a paper subsequently published in Physical Review D. Uploaded in accordance with the publisher's self-archiving policy. |
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 14:29 |
Last Modified: | 10 Oct 2019 02:06 |
Status: | Published |
Publisher: | American Physical Society (APS) |
Refereed: | Yes |
Identification Number: | 10.1103/physrevd.88.064026 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:151746 |