General Relativity

This chapter on general relativity begins by stating the basic property of gravitational fields. Explaining the space–time metric or metric tensor and curved space–time, it shows that whereas in the special theory of relativity one can define a reference frame by a set of bodies at rest in unchanging relative positions, such sets of bodies cannot exist in the general theory. Products of tensors, contraction of tensors, and tensor inverses are explained. Other useful concepts discussed include a geodesic and the Ricci tensor. Equations for the components of the Ricci curvature tensor in terms of the energy–momentum-density tensor are the Einstein field equations. By first solving Einstein's field equations in the case of a weak gravitational field (that is, one in which space–time has small curvature), it is possible to derive the famous Newtonian gravitational potential. The chapter ends with the derivation of Newton's law of gravitational attraction.