World function and time transfer: general post-Minkowskian expansions

In suitably chosen domains of space-time, the world function may be a powerful tool for modelling the deflection of light and the time/frequency transfer. In this paper we work out a recursive procedure for expanding the world function into a perturbative series of ascending powers of the Newtonian...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 21; no. 18; pp. 4463 - 4483
Main Authors Poncin-Lafitte, Christophe Le, Linet, Bernard, Teyssandier, Pierre
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 21.09.2004
Institute of Physics
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Summary:In suitably chosen domains of space-time, the world function may be a powerful tool for modelling the deflection of light and the time/frequency transfer. In this paper we work out a recursive procedure for expanding the world function into a perturbative series of ascending powers of the Newtonian gravitational constant G. We show rigorously that each perturbation term is given by a line integral taken along the unperturbed geodesic between two points. Once the world function is known, it becomes possible to determine the time transfer functions giving the propagation time of a photon between its emission and its reception. We establish that the direction of a light ray as measured in the 3-space relative to a given observer can be derived from these time transfer functions, even if the metric is not stationary. We show how to deduce these functions up to any given order in G from the perturbative expansion of the world function. To illustrate the method, we carry out the calculation of the world function and of the time transfer function outside a static, spherically symmetric body up to the order G^2, the metric containing three arbitrary parameters.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/21/18/012