Second post-Newtonian approximation of Einstein-aether theory

Understand

In this paper, second post-Newtonian approximation of Einstein-aether theory is obtained by Chandrasekhar's approach.

• Five parameterized post-Newtonian parameters in first post-Newtonian approximation are presented after a time transformation and they are identical with previous works, in which $\gamma=1$, $\beta=1$ and two preferred-frame parameters remain.
• Meanwhile, in second post-Newtonian approximation, a parameter, which represents third order nonlinearity for gravity, is zero the same as in general relativity.
• For an application for future deep space laser ranging missions, we reduce the metric coefficients for light propagation in a case of $N$ point masses as a simplified model of the solar system.