Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-03-23
Class.Quant.Grav. 21 (2004) 4463-4484
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Introduction is rewritten ; 2 references are added. 22 pages, no figure
Scientific paper
10.1088/0264-9381/21/18/012
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.
Le Poncin-Lafitte Christophe
Linet Bernard
Teyssandier Pierre
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