Lemaitre-Tolman-Bondi solutions in the Newtonian gauge: from strong to weak fields

Journal Article · Wed Oct 15 04:00:00 EDT 2008 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2008/10/028· OSTI ID:22156786

Lemaitre-Tolman-Bondi (LTB) solutions are used frequently to describe the collapse or expansion of spherically symmetric inhomogeneous mass distributions in the Universe. These exact solutions are obtained in the synchronous gauge where non-linear dynamics (with respect to the Friedmann-Lemaitre-Roberston-Walker (FLRW) background) induce large deviations from the FLRW metric. In this paper we show explicitly that this is a gauge artefact (for realistic sub-horizon inhomogeneities). We write down the non-linear gauge transformation from synchronous to Newtonian gauge for a general LTB solution using the fact that the peculiar velocities are small. In the latter gauge we recover the solution in the form of a weakly perturbed FLRW metric that is assumed in standard cosmology. Furthermore we show how to obtain the LTB solutions directly in Newtonian gauge and illustrate how the Newtonian approximation remains valid in the non-linear regime where cosmological perturbation theory breaks down. Finally we discuss the implications of our results for the backreaction scenario.

• OSTI ID: 22156786
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 10 Vol. 2008; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
COSMOLOGY
EXACT SOLUTIONS
GAUGE INVARIANCE
MASS DISTRIBUTION
METRICS
NONLINEAR PROBLEMS
PERTURBATION THEORY
SPHERICAL CONFIGURATION
STRONG INTERACTIONS
WEAK INTERACTIONS