Albert Einstein announces the next Cape Cod Astronomical Society meeting at Werner Schmidt Observatory. (astro humor)
In most circumstances in the universe, such time dilation is miniscule, but it can become very significant when spacetime is curved by a massive object such as a black hole. For example, an observer far from a black hole would observe time passing extremely slowly for an astronaut falling through the hole's boundary. In fact, the distant observer would never see the hapless victim actually fall in. His or her time, as measured by the observer, would appear to stand still. The slowing of time near a very simple black hole has been simulated on supercomputers at NCSA and visualized in a computer-generated animation.
__Gravitational Time Dilation__

Einstein's Special Theory of Relativity predicted that time does not flow at a fixed rate: moving clocks appear to tick more slowly relative to their stationary counterparts. But this effect only becomes really significant at very high velocities that app roach the speed of light.
When "generalized" to include gravitation, the equations of relativity predict that gravity, or the curvature of spacetime by matter, not only stretches or shrinks distances (depending on their direction with respect to the gravitational field) but also w ill appear to slow down or "dilate" the flow of time.

The general theory of relativity (GTR) and general relativity theory (GRT) is the geometrical theory of gravitation published by Albert Einstein before World War I. It unifies special relativity and Sir Isaac Newton's law of universal gravitation with the insight that gravitation is not due to a force but rather is a manifestation of curved space and time, with this curvature being produced by the mass-energy and momentum content of the space-time. General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate space-time content and space-time curvature.

General relativity is currently the most successful gravitational theory, being almost universally accepted and well confirmed by observations. The first success of general relativity was in explaining the anomalous perihelion precession of Mercury. Then in 1919, Sir Arthur Eddington announced that observations of stars near the eclipsed Sun confirmed general relativity's prediction that massive objects bend light. Since then, many other observations and experiments have confirmed many of the predictions of general relativity, including gravitational time dilation, the gravitational redshift of light, signal delay, and gravitational radiation. In addition, numerous observations are interpreted as confirming the weirdest prediction of general relativity, the existence of black holes.

In the mathematics of general relativity, the Einstein field equations become a set of simultaneous differential equations which are solved to produce metric tensors of space-time. These metric tensors describe the shape of the space-time, and are used to obtain the predictions of general relativity. The connections of the metric tensors specify the geodesic paths that objects follow when traveling inertially. Important solutions of the Einstein field equations include the Schwarzschild solution (for the space-time surrounding a spherically symmetric uncharged and non-rotating massive object), the Reissner-Nordström solution (for a charged spherically symmetric massive object), and the Kerr metric (for a rotating massive object).