A new approach to initial value variables for the Lemaître-Tolman-Bondi dust solutions

Authors: Sussman R.A.¹; Trujillo L.G.²

Source: Classical and Quantum Gravity, Volume 19, Number 11, 2002 , pp. 2897-2925(29)

Publisher: IOP Publishing

Abstract:

We re-examine the Lemaître-Tolman-Bondi (LTB) dust solutions by considering as free parameters the initial value functions: Yi, _i, ⁽³⁾_i, obtained by restricting the curvature radius, Y, the rest mass density, , and the three-dimensional Ricci scalar of the rest frames, ⁽³⁾, to an arbitrary regular Cauchy hypersurface, _i, marked by constant cosmic time (tti). Assuming the existence of symmetry centres, we use Yi to fix the radial coordinate and the topology (homeomorphic class) of _i, while the time evolution is described in terms of an adimensional scale factor yY/Yi. We show that the dynamics, regularity conditions and geometric features of the models are determined by _i, ⁽³⁾_i and by suitably constructed volume averages and contrast functions expressible in terms of invariant scalars defined in _i. These quantities lead to a straightforward characterization of initial conditions in terms of the nature of the inhomogeneity of _i, as density and/or curvature overdensities (`lumps') and underdensities (`voids') around a symmetry centre. In general, only models with initial density and curvature lumps evolve without shell-crossing singularities, though special classes of initial conditions, associated with a simultaneous big bang, allow for a regular evolution for initial density and curvature voids. Specific restrictions are found so that a regular evolution for tti is possible for initial voids. A brief guideline is provided for using the new variables in the construction of LTB models and for plotting all relevant quantities.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Instituto de Ciencias Nucleares, Apartado Postal 70543, UNAM, México DF 04510, México 2: Instituto de Física, Universidad de Guanajuato, Leon, Guanajuato, México

Publication date: 2002-01-01

• In this: publication
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• In this Subject: Nuclear Physics
• By this author: Sussman R.A. ;  Trujillo L.G.

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