Editing General relativity (section)

=== Definition and basic properties ===
General relativity is a [[metric (general relativity)|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 [[Stress–energy tensor|energy–momentum]] contained in that spacetime.<ref>{{Harvnb|Wald|1984|loc=ch. 4}}, {{Harvnb|Weinberg|1972|loc=ch. 7}} or, in fact, any other textbook on general relativity</ref> Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as [[free-fall]], orbital motion, and [[spacecraft]] [[Trajectory|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.<ref>At least approximately, cf. {{Harvnb|Poisson|2004a}}</ref> 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.<ref>{{Harvnb|Wheeler|1990|p=xi}}</ref>

While general relativity replaces the [[scalar field|scalar]] gravitational potential of classical physics by a symmetric [[Tensor#As multidimensional arrays|rank]]-two [[tensor]], the latter reduces to the former in certain [[Correspondence principle#Other scientific theories|limiting cases]]. For [[weak-field approximation|weak gravitational fields]] and [[slow-motion approximation|slow speed]] relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation.<ref>{{Harvnb|Wald|1984|loc=sec. 4.4}}</ref>

As it is constructed using tensors, general relativity exhibits [[general covariance]]: its laws—and further laws formulated within the general relativistic framework—take on the same form in all [[coordinate system]]s.<ref>{{Harvnb|Wald|1984|loc=sec. 4.1}}</ref> Furthermore, the theory does not contain any invariant geometric background structures, i.e. it is [[Background independence|background independent]]. It thus satisfies a more stringent [[general principle of relativity]], namely that the [[Physical law|laws of physics]] are the same for all observers.<ref>For the (conceptual and historical) difficulties in defining a general principle of relativity and separating it from the notion of general covariance, see {{Harvnb|Giulini|2007}}</ref> [[Local spacetime structure|Locally]], as expressed in the equivalence principle, spacetime is [[Minkowski space|Minkowskian]], and the laws of physics exhibit [[local Lorentz invariance]].<ref>section 5 in ch. 12 of {{Harvnb|Weinberg|1972}}</ref>