<P> There are alternatives to general relativity built upon the same premises, which include additional rules and / or constraints, leading to different field equations . Examples are Whitehead's theory, Brans--Dicke theory, teleparallelism, f (R) gravity and Einstein--Cartan theory . </P> <P> The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model - building . </P> <P> General relativity is a metric theory of gravitation . At its core are Einstein's equations, which describe the relation between the geometry of a four - dimensional, pseudo-Riemannian manifold representing spacetime, and the energy--momentum contained in that spacetime . Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free - fall, orbital motion, and spacecraft trajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths . Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest - possible paths that objects will naturally follow . The curvature is, in turn, caused by the energy--momentum of matter . Paraphrasing the relativist John Archibald Wheeler, spacetime tells matter how to move; matter tells spacetime how to curve . </P> <P> While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank - two tensor, the latter reduces to the former in certain limiting cases . For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation . </P>

Space and time in general theory of relativity