Luminosity distance-redshift relation for the LTB solution near the center

Details Luminosity distance-redshift relation for the LTB solution near the center Luminosity distance-redshift relation for the LTB solution near the center

2007-03-02

arxiv.org/abs/gr-qc/0703012v2

Class.Quant.Grav.24:3843-3857,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 2 figures, including 2 new paragraphs and 1 figure in section 2, final version to appear in Classical and Quantum Gr

Scientific paper

10.1088/0264-9381/24/15/006

Motivated by the inverse problem for the Lemaitre-Tolman-Bondi dust solution, in which problem the luminosity distance function $D_L(z)$ is taken as an input to select a specific model, we compute the function $D_L(z)$ of the LTB solution up to the third order of $z$. To perform the otherwise cumbersome computation, we introduce a new convenient form of the LTB solution, in which the solution is explicit and unified. With this form of the LTB solution we obtain the luminosity distance function with the full generality. We in particular find that the function exactly coincides with that of a homogeneous and isotropic dust solution up to second order, if we demand that the solution be regular at the center.

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