General post-Minkowskian expansion of time transfer functions

Details General post-Minkowskian expansion of time transfer functions General post-Minkowskian expansion of time transfer functions

2008-03-03

arxiv.org/abs/0803.0277v3

Class.Quant.Grav.25:145020,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages. Minor modifications. Accepted in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/25/14/145020

Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant $G$ (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

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