In newtonian mechanics, As far as I'm aware, only kinetic energy is dependent on frames of reference, since kinetic energy is a function of velocity(squared) and velocity is dependent on frames of reference, therefore kinetic energy is frame dependent.

In newtonian mechanics, assuming that all observers use the same reference for zero potential energy($U=0$), it's frame independent . Potential energy of point particles in force fields, like gravity and electric field are given by: $U=constant\dfrac{\xi\_1\xi\_2}{r}$, where $\xi$ is either the gravitational or the electric charge of a particle. Since both charges and the distance $r$ between them is invariant under all frames of reference, therefore potentential energy is frame independent.

In SR, one expects that the potential energy of an object in a force field should also be a function of the charges and the distance between them. However since the distance $r$ between the charges is relative to the choice of the frame of reference(it's $r$ in a rest frame and $\dfrac{r}{\gamma}$ in a frame that's moving relative to the two charges, owing to lorentz contraction), therefore it seems to me that potential energy becomes frame dependent in SR. 

Is this the case?