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 γ=1 as in the previous research. We find two remarkable things for other parameters. The first is the value β=1, while it has been reported that β≠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 α₁ and α₂. 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.