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World function and time transfer: general post-Minkowskian expansions

Christophe Le Poncin-Lafitte·Bernard Linet·Pierre Teyssandier
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Abstract

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.

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Christophe Le Poncin-Lafitte, Bernard Linet, Pierre Teyssandier. 2004-08-03. World function and time transfer: general post-Minkowskian expansions. https://doi.org/10.1088/0264-9381%2F21%2F18%2F012

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