Post-Newtonian parameters in the tensor-vector-scalar theory

TL;DR

This paper analyzes post-Newtonian parameters in the tensor-vector-scalar (TeVeS) theory beyond spherical symmetry, finding that certain parameters match general relativity and discussing implications for stability and perturbations.

Contribution

It extends previous TeVeS analyses to general settings, revealing that mma=1, eta=1 under specific assumptions, and discusses the static nature of the Newtonian potential and its implications.

Findings

mma=1 as in previous studies

eta=1 under the assumption of Minkowski metrics

The Newtonian potential must be static for consistency

Abstract

We investigate post-Newtonian parameters in the tensor-vector-scalar (TeVeS) theory in a general setting while previous researches have been restricted to spherically symmetric cases. Based on the assumption that both the physical and Einstein metrics have Minkowski metric at the zeroth order, we show $\gamma =1$ as in the previous researches. We find two remarkable things for other parameters. The first is the value $\beta =1$ while it has been reported that $\beta\neq 1$ for the case when the vector field is not purely timelike. This discrepancy occurs from the above assumption which is natural as a starting point. The second is the result that the Newtonian potential must be static to be consistent with the vector equation. As a result, we cannot determine $\alpha_{1}$ and $\alpha_{2}$. We consider that it is related to the instability against linear perturbation and occurrence of caustic singularities for various initial perturbations which have been reported recently.