Abstract
In this chapter we begin the study of the gravitational fields in the framework of the general theory of relativity. The force of gravity is an unscreened long-range force, and it can be considered as an intrinsic property of the space-time related to the space-time geometry. We, therefore, start by studying the time intervals and distances in the pseudo-Riemannian metric of the general relativity. Then we study the motion of particles in the gravitational fields using the geodesic equations of motion, whereby we find the approximate relation between the temporal metric tensor component and the non-relativistic potential of the gravitational field. Finally, we study the electromagnetic field equations in the presence of gravitational fields.
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