General post-Minkowskian expansion of time transfer functions

TL;DR

This paper introduces a recursive, self-sufficient method to expand time transfer functions in general relativity into a post-Minkowskian series, simplifying calculations for light travel times without solving geodesic equations.

Contribution

A novel recursive procedure for expanding time transfer functions in powers of G, avoiding integration of geodesic equations or Synge's world function.

Findings

Derived the time transfer function for a family of static, spherically symmetric metrics.

Provided a post-linear approximation example.

Simplified the computation of light travel times in relativistic tests.

Abstract

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.