Parametrized post-post-Newtonian analytical solution for light propagation

Abstract

An analytical solution for light propagation in the post-post-Newtonian approximation is given for the Schwarzschild metric in harmonic gauge augmented by PPN and post-linear parameters $\beta$, $\gamma$ and $\epsilon$. The solutions of both Cauchy and boundary problem are given. The Cauchy problem is posed using the initial position of the photon $\ve{x}_0 = \ve{x}(t_0)$ and its propagation direction \veσ at minus infinity: $\veσ = {1\over c} \lim\limits_{t \to -\infty}\dot{\ve{x}}(t)$. An analytical expression for the total light deflection is given. The solutions for $t-t_0$ and $\veσ$ are given in terms of boundary conditions $\ve{x}_0 = \ve{x} (t_0)$ and $\ve{x} = \ve{x}(t)$.

12 pages, 0 figures, Report of astrometric mission GAIA

Cited by in corpus (1)

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