## Abstract

Motivated by the inverse problem for the Lematre-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 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 centre.

Original language | English |
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Article number | 006 |

Pages (from-to) | 3843-3857 |

Number of pages | 15 |

Journal | Classical and Quantum Gravity |

Volume | 24 |

Issue number | 15 |

DOIs | |

Publication status | Published - Aug 8 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)