Einstein discovered that he could relate 10 of these components in a natural way to the sources of the gravitational field, mass (or energy), density, momentum density, and stress, if he were to duplicate approximately Newton's equations of the gravitational field and, at the same time, formulate laws that would take the same form regardless of the choice of frame of reference. The remaining 10 components may be chosen arbitrarily at any one point but are related to each other by partial differential equations at neighbouring points. Einstein derived a field equation that, along with the rule that a freely falling body moves along a geodesic, forms the comprehensive treatment of gravitation known as the general theory of relativity.

The general theory of relativity is constructed so that its results are approximately the same as those of Newton's theories as long as the velocities of all bodies interacting with each other gravitationally are small compared with the speed of light--i.e., as long as the gravitational fields involved are weak. The latter requirement may be stated roughly in terms of the escape velocity. The escape velocity is defined as the minimal speed with which a projectile must be endowed at any given location to enable it to fly off to infinitely removed regions of the universe without the application of further force. On the surface of the Earth the escape velocity is approximately 11.2 kilometres (6.95 miles) per second. A gravitational field is considered strong if the escape velocity approaches the speed of light, weak if it is much smaller. All gravitational fields encountered in the solar system are weak in this sense.

The success of Newton's theory, incidentally, must be considered a confirmation of the general theory of relativity to the extent that that application of the theory remains confined to situations involving small relative speeds and weak fields. Obviously, any superiority of the new theory over the old one may be inferred only if their predictions disagree and if those of the general theory of relativity are confirmed by experiment and observation.

As the principle of equivalence forms the cornerstone of general relativity, its verification is crucial. Highly precise experiments with this objective were performed between 1888 and 1922 by a Hungarian physicist, Roland, Baron von Eötvös, and his collaborators, who confirmed the principle to an accuracy of one part in 10⁸, and in the 1960s by an American physicist, Robert Dicke, who achieved an accuracy of one part in 10¹¹. Subsequently the Soviet physicist V.L. Braginsky further improved the accuracy to one part in 10¹². Through this work the principle of equivalence has become one of the most precisely confirmed general principles of contemporary physics.

Some other new predictions of general relativity are explained below.