Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-04-06
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, one figure. Comments are welcome. Numerical module for evaluation of the solutions will be released at http://web.
Scientific paper
We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.
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