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Even at this level of examination, the fundamental thesis of the general theory of relativity is obvious: motion is determined by the curvature of spacetime, and the curvature of spacetime is determined by the matter, energy, momentum and fields within it.

In the [[Law of Universal Gravitation|Newtonian approximation]], the gravitational vector field is directly proportional to mass. In general relativity, mass is just one of several sources of spacetime curvature. The ''stress-energy tensor,'' <math>T_{\mu\nu}</math>, includes all of these sources. Put simply, the stress-energy tensor quantifies all the ''stuff'' that contributes to spacetime curvature, and thus to the gravitational field.

In this way, we can see that the stress-energy tensor neatly quantifies ''all'' static and dynamic properties of a region of spacetime, from mass to momentum to electric charge to temperature to pressure to shear stress. Thus, the stress-energy tensor is all we need on the right-hand side of the equation in order to relate matter, energy and, well, ''stuff'' to curvature, and thus to the gravitational field.

===The left side of the equation: the Einstein curvature tensor===