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Prescriptions for measuring and transporting local angular momenta in general relativity

Flanagan, Éanna É. and Nichols, David A. and Stein, Leo C. and Vines, Justin (2016) Prescriptions for measuring and transporting local angular momenta in general relativity. Physical Review D, 93 (10). Art. No. 104007. ISSN 2470-0010. https://resolver.caltech.edu/CaltechAUTHORS:20160525-130620865

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Abstract

For observers in curved spacetimes, elements of the dual space of the set of linearized Poincaré transformations from an observer’s tangent space to itself can be naturally interpreted as local linear and angular momenta. We present an operational procedure by which observers can measure such quantities using only information about the spacetime curvature at their location. When applied by observers near spacelike or null infinity in stationary, vacuum, asymptotically flat spacetimes, there is a sense in which the procedure yields the well-defined linear and angular momenta of the spacetime. We also describe a general method by which observers can transport local linear and angular momenta from one point to another, which improves previous prescriptions. This transport is not path independent in general, but becomes path independent for the measured momenta in the same limiting regime. The transport prescription is defined in terms of differential equations, but it can also be interpreted as parallel transport in a particular direct-sum vector bundle. Using the curvature of the connection on this bundle, we compute and discuss the holonomy of the transport law. We anticipate that these measurement and transport definitions may ultimately prove useful for clarifying the physical interpretation of the Bondi-Metzner-Sachs charges of asymptotically flat spacetimes.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevD.93.104007DOIArticle
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.93.104007PublisherArticle
https://arxiv.org/abs/1602.01847arXivDiscussion Paper
ORCID:
AuthorORCID
Stein, Leo C.0000-0001-7559-9597
Additional Information:© 2016 American Physical Society. Received 4 February 2016; published 3 May 2016. L. C. S. acknowledges that support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award No. PF2–130101 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under Contract No. NAS8–03060, and further acknowledges support from NSF Grant No. PHY–1404569. E. E. F. and D. A. N. acknowledge support of NSF Grants No. PHY–1404105 and No. PHY–1068541.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NASA Eistein Postdoctoral FellowshipPF2-130101
NASANAS8-03060
NSFPHY-1404569
NSFPHY-1404105
NSFPHY-1068541
Issue or Number:10
Record Number:CaltechAUTHORS:20160525-130620865
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160525-130620865
Official Citation:Prescriptions for measuring and transporting local angular momenta in general relativity Éanna É. Flanagan, David A. Nichols, Leo C. Stein, and Justin Vines Phys. Rev. D 93, 104007 – Published 3 May 2016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67352
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 May 2016 16:53
Last Modified:09 Mar 2020 13:19

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