EM fields and space time?

Instead of calculating relative mass and density of an object to quantify gravity and gravitational forces, could Em field density be inserted into these calcs? why the shift from EM to Gr, relative to size? I know string theory is all the rage for unification, but why complicate an already complicated theory with more theory?
Sure, you can add the energy density on the right hand side of the Poisson equation. However, this is not covariant under Lorentz transformation, and, much worse, it doesn't hold up empirically.

Also, you might take a look at Nordström's attempt at a scalar theory of gravity:


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