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  Relativistic Lagrangian displacement field and tensor perturbations

Rampf, C., & Wiegand, A. (2014). Relativistic Lagrangian displacement field and tensor perturbations. Physical Review D, 90: 123503. doi:10.1103/PhysRevD.90.123503.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0023-CE74-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-7676-C
Genre: Journal Article

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 Creators:
Rampf, Cornelius, Author
Wiegand, Alexander1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO
 Abstract: We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the fundamental Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully non-perturbative approach based on the ADM split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the non-perturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve for gravitational waves in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious tensor artefacts at second order, in both the Lagrangian and Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the non-linear frame-dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a $\Lambda$CDM Universe in the attendance of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.

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 Dates: 2014-09-052014
 Publication Status: Published in print
 Pages: 20 pages, two figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1409.2688
DOI: 10.1103/PhysRevD.90.123503
 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: 90 Sequence Number: 123503 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258