Instead of the space time I prefer the dynamic vacuum field for explanations of the gravitation and action of electric forces. See the papers https://www.researchgate.net/publication/284032224_The_Graviton_Field_as_the_Source_of_Mass_and_Gravitational_Force_in_the_Modernized_Le_Sage%27s_Model
Electromagnetic energy is contained in the electromagnetic stress energy tensor which enters into Einstein Field Equations. The full set of Maxwell equations does not emerge from 4 dimensions, but does emerge from 5 dimensions.
For your answer, a system of 4 dimensions is not large enough to merge Einstein equations with Maxwell equations unless they are entered separately.
I wonder why lows of motion cant be fix to explain simple attraction and repulsive motions in basic levels !!!!!!!!!!!!!. Space time curvature can moves the objects without force ...i think that elector statics attraction and repulsiveness can be fix same as gravity
The electromagnetic interaction is independent of the spacetime and gravitation, which depends of the spacetime, are independent physical interactions in spite of the similarities between Coulomb and Newton laws . In fact what we know is that the repulsion or the attraction of electric charges is due to Coulomb law at macroscopic level, and at microscopic level this interaction is due to virtual photons. What is the reason that chages of the same sign repel while the ones with different sign attract? Nobody knowns, as it happens with gravitation where only attraction between masses is allowed and no repulsion exists.
There is no meaning for gravitational faces or electromagnetic interaction forces .We can use space time curvature to move partials attractive or repulsive way . Because what you feel force is not forces but masses moves in geodesics of space time curves .!
The spacetime curvature associated to electrodynamics is zero and obviously this cannot explain any attraction or repulsion between two electric charges. On the other hand if you use the energy-momentum tensor due to electrodynamics within gravitational Einstein's equations, this is going to give you one small value of the curvature if you don't employ cosmological scales of charged bodies.