Gertsenshtein gives a clear equation describing the relationship between electromagnetic energy and gravitational waves. The equation used to calculate the amplitude of the gravitational wave is (Gertsenshtein, 1962)
\[\frac{a(x)}{b} = \sqrt{\frac{\gamma}{\pi c^3} F^{(0)2} R_{0} T},\]
where \(F\) represents electromagnetic energy in gauss, \(R_{0}\) represents the distance from the EM source in meters, and \(T\) is the time allotted for gravitational radiation in years.
There is supporting mathematics that the relationship can be reversed. When an EMW \((E, H)\) propagates in the field \(H_0\) there appears a stress tensor proportional to \(HH_0\) which is variable in space and time. This tensor is the source of GW. When a GW propagates through the field \(H_0\) there occurs a stretching and compression of the magnetic field, accompanied by the appearance of an alternating magnetic field \(h(x, t)H_0\), where h is the variation of the metric in the GW. The field \(hH_o\) is the source for the EMW and it is obvious a medium mediates the conversion process (Zel’dovich, 1973; Mitskevich et al., 1969; Boccaletti et al., 1970; Dubrovich et al., 1972).
The investigation into \(H_0\) and the reversal of Gerstenshtein’s equation also supports our earlier assumption that we could derive an equation in the Post-Newtonian form describing time varying gravitational potential, \(\phi\), from an electromagnetic field. Interestingly, Zel’dovich considered the conversion of EMW to GW to be so trivial that in the presence of matter it was undetectable.