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Maxwell's equations and general relativity—what are these all about?

Maxwell's equations are the key linear partial differential equations that describe classical electromagnetism. The equations relate the electromagnetic field to currents and charges. On the other hand, in general relativity, the Einstein field equation is a set of nonlinear partial differential equations describing how the metric of spacetime evolves, given some conditions, such as mass density in the spacetime. Both equations are ultimately of second order, if seen properly.

Therefore, we thought that perhaps we are talking about the same governing equation, which could describe both electromagnetism and gravitation. Indeed, it becomes clear that Maxwell's equations hide inside the Einstein field equations of general relativity. The metric tensor of spacetime tells us how lengths determine in spacetime. The metric tensor also thus determines the curvature properties of spacetime. Curvature is what we feel as "force." In addition, energy and curvature relate to each other through the Einstein field equations. Test particles follow what are called geodesics—the shortest paths in the spacetime.