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A geometric description of equivalence principle physics of gravitational time dilation is presented. In this geometric theory, the metric plays the role of relativistic gravitational potential. Einstein proposed curved spacetime as the gravitational field. The geodesic equation in spacetime is the GR equation of motion, which is checked to have the correct Newtonian limit. At every spacetime point, one can construct a free-fall frame in which gravity is transformed away. However, in a finite-sized region, one can detect the residual tidal force which is second derivative of gravitational potential. It is the curvature of spacetime. The GR field equation directly relates the mass/energy distribution to spacetime's curvature. Its solution is the metric function, determining the geometry of spacetime.

*Keywords: *
geometric theory;
gravity;
time dilation;
metric as potential;
curved spacetime;
geodesic equation;
Newtonian limit;
tidal force;
Einstein equation

*Chapter.*
*8608 words.*
*Illustrated.*

*Subjects: *
Astronomy and Astrophysics

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