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

We investigate post-Newtonian parameters in the tensor-vector-scalar theory in a general setting while previous research has been restricted to spherically symmetric cases. Based on the assumption that both the physical and Einstein metrics have a Minkowski metric at the zeroth order, we show $\gamma =1$ as in the previous research. We find two remarkable things for other parameters. The first is the value $\beta =1$, while it has been reported that $\beta \ne 1$ 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.