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Article Dans Une Revue Classical and Quantum Gravity Année : 2013

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

Résumé

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.

Dates et versions

hal-00815626 , version 1 (19-04-2013)

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Citer

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, 2013, 30 (17), pp.175008. ⟨10.1088/0264-9381/30/17/175008⟩. ⟨hal-00815626⟩
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