Second post-Newtonian approximation of Einstein-aether theory

TL;DR

This paper derives the second post-Newtonian approximation of Einstein-aether theory, confirming some parameters match general relativity and providing a model for light deflection relevant to future space missions.

Contribution

It extends the post-Newtonian approximation of Einstein-aether theory to second order, including light propagation modeling for solar system tests.

Findings

Second post-Newtonian parameters match previous first order results.

A third order nonlinearity parameter is zero, same as in general relativity.

Derived light deflection angle constrains Einstein-aether theory.

Abstract

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. The resulting light deflection angle in second post-Newtonian approximation poses another constraint on the Einstein-aether theory.