Justin Long edited subsection_Post_Newtonian_Approximation_of__.tex  over 8 years ago

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\nabla\cdot{S}+\frac{\partial U}{\partial t} = \frac{4}{c^4}U\frac{\partial \phi^2}{\partial t},  \end{equation}  where use has been made of the Poynting vector, $S = \frac{c}{4π}E × B$, and the factor of $c$ has been reinstated to illustrate the order of magnitude of this effect. This demonstrates that in a region of nonzero internal energy density $U$ and rapidly time varying gravitational potential, $φ$, $\phi$,  electromagnetic radiation will be generated. Using the theory of equivalence, we assume that the relationship can be reversed. By solving for the time varying gravitational potential, $φ$, $\phi$,  we show that electromagnetic radiation gives rise to a time varying spacetime metric. \begin{equation}  \phi = \frac{c^2}{2}\sqrt{\int\frac{\nabla\cdot{S}}{U}\frac{\partial U}{\partial t}}  \end{equation} By having an equation that readily describes the relationship between spacetime warping and EM radiation, we can accurately predict results in experimental setups.