Second post-Newtonian approximation of 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.

29 pages, no figures

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Cited by in corpus (12)

• A Modified Scalar-Tensor-Vector Gravity Theory and the Constraint on its Parameters
• 2PN Light Propagation in the Scalar-Tensor Theory: an $N$-Point-Masses Case
• Kantowski-Sachs Einstein-æther perfect fluid models
• The Second Post-Newtonian Light Propagation and Its Astrometric Measurement in the Solar System
• Cosmological Evolution of Einstein-Aether Models with Power-law-like Potential
• Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem
• Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem
• Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem
• Post-linear metric of a compact source of matter
• Might the 2PN perihelion precession of Mercury become measurable in the next future?
• Parameterized second post-Newtonian framework with conservation Laws
• Leading-order gravitational time delay of massive particles by a moving Schwarzschild lens