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New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order G 3

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00815626
Contributor : Bernard Linet <>
Submitted on : Friday, April 19, 2013 - 9:56:18 AM
Last modification on : Thursday, April 2, 2020 - 1:28:26 PM

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Bernard Linet, Pierre Teyssandier. New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order G 3. Classical and Quantum Gravity, IOP Publishing, 2013, 30 (17), pp.175008. ⟨10.1088/0264-9381/30/17/175008⟩. ⟨hal-00815626⟩

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