# Why is there not a General Relativity for forces other than gravity?

I think what I'm looking for here is some sort of a bridge between the very material terms and mental images that I have access to and more of a pure math understanding. My deepest exposure to abstractions in math is constructing vectors from their properties in linear algebra--so I understand what it looks like to uncover the form of an object from the way it interacts with other elements of math. I don't have a connection between that way of thinking and physics, though; my deepest connection to physics essentially amounts to curve-fitting. So I suppose these kinds of questions are hard to ask in an interesting way, and if there's a mathematical foundation that would help me think productively about what it means or doesn't mean to describe physics--I'd appreciate hearing about it.

My understanding of GR is that it details how gravity can be modeled by describing spacetime with geometric equations and deriving motion from those:

$$R_{\mu \nu} - {1 \over 2}R \, g_{\mu \nu} + \Lambda g_{\mu \nu}= {8 \pi G \over c^4} T_{\mu \nu}$$

the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of space-time with the distribution of matter within it. (Wikipedia)

Not just matter, but the above equation appears to relate the energy of other forces, i.e. electromagnetism, as directly contributing to the curvature of space and therefore motion due to gravitation.

Meanwhile, nowhere in the equations for electricity and magnetism do I see any geometric relation to spacetime; they appear to be properties in space rather than properties of space.

If GR relates electromagnetic energy to spacetime curvature, why do we not have any geometric description of the electromagnetic forces like we have for gravity? Does this imply that

• all of these forces are abstractly distinct objects, whose behavior can't be generalized together instead of separately; or
• there may be a description for electromagnetism similar to GR, but we haven't found it?

I interpret the unification of physics as implying that there is an abstract object of which all of these are properties, and that those separate properties can be derived from a more general description of that unitary object's nature. If that's an accurate picture, do we have any reason to think that it's true? Or will finding such a unifying principle be the sole reason to suspect that it's possible to generalize across these forces?