Equiangular polygon

Einstein's theory of general relativity (1915) stated that the presence of mass, energy, and momentum causes spacetime to become curved. Because of this curvature, the paths that objects in inertial motion follow can "deviate" or change direction over time. This deviation appears to us as an acceleration towards massive objects, which Newton characterized as being gravity. In general relativity however, this acceleration or free fall is actually inertial motion. So objects in a gravitational field appear to fall at the same rate due to their being in inertial motion while the observer is the one being accelerated. (This identification of free fall and inertia is known as the Equivalence principle.)

The Einstein field equations can be written briefly in abstract index notation as rank 2 symmetric tensors:

$G_{ab}=8\pi T_{ab}$

where $G_{ab}$ is the curvature of spacetime and $T_{ab}$ is the stress-energy within it. Many exact solutions of the Einstein field equations are known. The solutions to the field equations are metrics of spacetime. These metrics describe the structure of spacetime given the stress-energy and coordinate mapping used to obtain that solution.