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Gravitational field from virtual photons; does $\rho c^2 = \frac{1}{2} \epsilon_0 E^2$?

Answers to Is Energy Localised in space? got me thinking about answer(s) to Sun constantly converts mass into energy, will this cause its gravity to decrease? and the contribution to the Sun's gravity by the energy of the real photons slowly making their way out of the Sun (small but interesting).

As a gedankenexperiment, I make a strong electric field $E$ (of virtual photons) of a particular shape by bringing two or more charges close together, and then map the apparent gravitational field (distortion of space-time) around it and then calculate a hypothetical "mass distribution" $\rho$ that would produce such a field.

Would the calculated "mass density" reflect the actual energy denstiy as $\rho c^2 = \frac{1}{2} \epsilon_0 E^2$?

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