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Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...
Velocity and gravitational time dilation have been the subject of science fiction works in a variety of media. Some examples in film are the movies Interstellar and Planet of the Apes . [ 43 ] In Interstellar , a key plot point involves a planet, which is close to a rotating black hole and on the surface of which one hour is equivalent to seven ...
By definition, an affine connection is a bilinear map () (), where () is a space of all vector fields on the spacetime. This bilinear map can be described in terms of a set of connection coefficients (also known as Christoffel symbols ) specifying what happens to components of basis vectors under infinitesimal parallel transport: ∇ e i e j ...
It is an attribute of matter, radiation, and non-gravitational force fields. The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity. Because this tensor has 2 indices (see next section) the Riemann ...
This gravitational frequency shift corresponds to a gravitational time dilation: Since the "higher" observer measures the same light wave to have a lower frequency than the "lower" observer, time must be passing faster for the higher observer. Thus, time runs more slowly for observers the lower they are in a gravitational field.
But time is weird, and there's another phenomenon called relative velocity time dilation that usurps gravity's effect. Why astronauts age slower Relative velocity time dilation is where time moves ...
[5] [8] A gravitational redshift can also equivalently be interpreted as gravitational time dilation at the source of the radiation: [8] [2] if two oscillators (attached to transmitters producing electromagnetic radiation) are operating at different gravitational potentials, the oscillator at the higher gravitational potential (farther from the ...
t r is the elapsed time for an observer at radial coordinate r within the gravitational field; t is the elapsed time for an observer distant from the massive object (and therefore outside of the gravitational field); r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object);