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  Frame dragging and Eulerian frames in General Relativity

Rampf, C. (2014). Frame dragging and Eulerian frames in General Relativity. Physical Review D, 89: 063509. doi:10.1103/PhysRevD.89.063509.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-7E51-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0019-8053-5
Genre: Journal Article

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 Creators:
Rampf, Cornelius1, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO,General Relativity and Quantum Cosmology, gr-qc
 Abstract: The physical interpretation of cold dark matter perturbations is clarified by associating Bertschinger's Poisson gauge with a Eulerian/observer's frame of reference. We obtain such an association by using a Lagrangian approach to relativistic cosmological structure formation. Explicitly, we begin with the second-order solution of the Einstein equations in a synchronous/comoving coordinate system---which defines the Lagrangian frame, and transform it to a Poissonian coordinate system. The generating vector of this coordinate/gauge transformation is found to be the relativistic displacement field. The metric perturbations in the Poissonian coordinate system contain known results from standard/Eulerian Newtonian perturbation theory, but contain also purely relativistic corrections. On sub-horizon scales these relativistic corrections are dominated by the Newtonian bulk part. These corrections however set up non-linear constraints for the density and for the velocity which become important on scales close to the horizon. Furthermore, we report the occurence of a transverse component in the displacement field, and find that it induces a non-linear frame dragging as seen in the observer's frame, which is sub-dominant at late-times and sub-horizon scales. Finally, we find two other gauges which can be associated with a Eulerian frame. We argue that the Poisson gauge is to be preferred because it comes with the simplest physical interpretation.

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 Dates: 2013-07-052013-11-1820142014
 Publication Status: Published in print
 Pages: 11 pages, results unchanged, extended discussion, submitted
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1307.1725
DOI: 10.1103/PhysRevD.89.063509
 Degree: -

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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 89 Sequence Number: 063509 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258