Eur. Phys. J. Plus (2013) 128: 107
https://doi.org/10.1140/epjp/i2013-13107-0

Regular Article

Lemaître-Tolman-Bondi model: Solutions of the cosmological equation

¹ Dipartimento di Fisica dell’Università degli Studi di Milano, Via Celoria, 16, 20133, Milano, Italy
² GNFM, Gruppo Nazionale per la Fisica Matematica, Sesto Fiorentino, Italy

Received: 20 June 2013
Accepted: 9 September 2013
Published online: 17 September 2013

Abstract

The solution of the generalized Newton-like equation of the Lemaître-Tolman-Bondi cosmological model with cosmological constant ( LTB) is reconsidered. Parametric solutions, obtained by different methods, are further elaborated by means of the properties of the Weierstrass elliptic functions. This allows significant new aspects of the solutions to be emphasized. Also factorized parametric solutions are determined by applying an integration method previously considered. The scalar, Dirac and spin 1 field equations become separable in the space-time given by the factorized parametric solutions.