Here is a high-level derivation how charge generates forces in fields that live on spacetime, I will dive deeper later on.

Force = exchange of gauge field quanta required by local symmetry, it is the price nature pays to keep symmetry local.

It naturally makes me connect charge to energy, if energy is generator of time shift, it could also cause some kind of force, in this case it is the gravity, which is Einstein’s general relativity, it’s consistent to Gravity as a gauge theory of spacetime symmetry.

But before trying to derive the theory of gravity, I need to refresh concept of field strength tensor Fμν​ and energy momentum tensor Tμν​.

Fμν is the electromagnetic field tensor, also called the field strength tensor. It packages the electric and magnetic fields into a single antisymmetric rank‑2 tensor on spacetime. In components (in suitable units), the time–space parts are the electric field and the space–space parts are the magnetic field: roughly $F_{0i}\sim E_i$F0i∼Ei and $F_{ij}\sim {ϵ}_{ijk}{B}_k$Fij∼ϵijkBk. It is defined from the four‑potential $A_{\mu }$Aμ by$$F_{\mu \nu }={\mathrm{\partial }}_{\mu }{A}_{\nu }-{\mathrm{\partial }}_{\nu }{A}_{\mu },$$Fμν=∂μAν−∂νAμ,which is the relativistic, coordinate‑free way to encode Maxwell’s field.

Tμν:

So: $T_{\mu \nu }$Tμν tells you about energy and momentum density/flux; $F_{\mu \nu }$Fμν tells you about the electromagnetic field itself (its electric and magnetic components) in a Lorentz‑covariant way.