Bernard Linet, Pierre Teyssandier
A new iterative method for calculating the travel time of a photon as a function of the spatial positions of the emitter and the receiver in the field of a static, spherically symmetric body is presented. The components of the metric are assumed to be expressible in power series in m/r, with m being half the Schwarzschild radius of the central body and r a radial coordinate. The procedure exclusively works for a light ray the parametric equations of which may be expanded in power series of the gravitational constant G. It is shown that the expansion of the travel time of a photon along such a ray only involves elementary integrals whatever the order of approximation. An expansion of the impact parameter in power series of G is also obtained. In order to illustrate the method, the perturbation terms are explicitly calculated up to the order G^3. The expressions yielding the third-order terms in the light travel time and the impact parameter are new results.
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http://arxiv.org/abs/1304.3683
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