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Justin Long edited subsection_Post_Newtonian_Approximation_of__.tex
over 8 years ago
Commit id: e0379f375ed32b5a6fbe9d278a89fcb802beec69
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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.