A dynamic transformation, unlike a static transformation, contains movement. The test particle is not stationary but moving through space and time. If the particle (against Einstein’s SR postulate) could move instantly with no time passage, then it would move through space without velocity, but that is not possible with any known experiment. Therefore, it is moving through space and time. Since the test particle is moving through space and time, a type of area (space X time) is being swept out as the particle moves, as previously shown. To properly transform this type of dynamic, a transformation of space (length) and temporal (time) must be performed on the particle’s trajectory. Thus, a motion about a circular path would be a sum of the potential for a change in time and the potential for a change in space. The following arc path transformation is used:
\begin{equation}
2 \pi r_{\mathcal{P}} \rightarrow 2 \pi \phi^{-1} r_{\mathcal{E}}
\end{equation}
Where \(\phi^{-1}\) is
\begin{equation}
\phi^{-1} = \left( 1 + \frac{G M}{r c^2} + \frac{G M}{r c^2} \right) = \left( 1 + \frac{2G M}{r c^2} \right)
\end{equation}