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Title: Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation

We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to the synchronous and comoving gauge and obtain the Lagrangian metric within the Newtonian approximation. Our approach is fully non-perturbative, which implies that if our quantities are expanded according to the rules of standard perturbation theory, all terms are exactly recovered at any order in perturbation theory, only provided they are Newtonian. We explicitly show this result up to second order and in both gauges. Our transformation clarifies the meaning of the change of spatial and time coordinates from the Eulerian to the Lagrangian frame in the Newtonian approximation.
Authors:
;  [1] ;  [2]
  1. Dipartimento di Fisica, Università di Milano, via Celoria 16, 20154 Milano (Italy)
  2. Dipartimento di Fisica e Astronomia ''G. Galilei", Università degli Studi di Padova and INFN Sezione di Padova, via Marzolo 8, 35131 Padova (Italy)
Publication Date:
OSTI Identifier:
22373509
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; COORDINATES; GENERAL RELATIVITY THEORY; LAGRANGIAN FUNCTION; METRICS; NONLINEAR PROBLEMS; PERTURBATION THEORY