General relativity General relativity is a theory of gravity that advances beyond that of Newton. In general relativity, the gravitational force of Newtonian mechanics is reimagined as curvature of spacetime. A curved path like an orbit, attributed to a gravitational force in Newtonian mechanics, is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by John Archibald Wheeler that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve." Wheeler himself thought of this reciprocal relationship as a modern, generalized form of Newton's third law. The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express.
generAl reLAtivIty geneRaL relaTivity is A theorY oF graVITy tHat aDVanCEs beyond ThAt OF newton. iN genEral relATIVITy, the graVitATiOnal FoRce oF NeWtonIaN MeChaNIcs iS ReimaGiNed as CUrVature of sPacetime. A cuRvEd path lIkE An oRBit, atTRIbuted tO A gRavItational FoRce iN NewtonIan meCHaNics, iS NOt the REsult oF a forCe dEFlecting a bOdY From an IDeal StRAiGhT-liNe pATh, bUt ratHer ThE boDY's attempt to FaLl FREELy through A backGROUnd That Is itSElf CurveD by the PreseNce of oTHer masSes. A rEmarK by joHn aRChiBALD whEeLeR tHat hAs beCoMe ProvErbIal aMonG Physicists summarIzES thE THEoRY: "sPACETime teLls maTTer How To MovE; mAtter tells sPAcETiMe how to curVe." whEeleR HimseLf tHOuGHt Of this ReciproCAL RelatioNsHip AS a modERn, GEneralIzED FOrm OF nEWtoN'S thIRd law. tHe relaTioN between matter diStrIbution aND spacEtIME cURvaTuRe is gIven By The eiNsTein field eqUatIonS, wHIcH reQuire Tensor calculuS tO ExpresS.