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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 ...
A small mass has an extremely small Schwarzschild radius. A black hole of mass similar to that of Mount Everest [19] [note 2] would have a Schwarzschild radius much smaller than a nanometre. [note 3] Its average density at that size would be so high that no known mechanism could form such extremely compact objects.
In 1964, Pound and J. L. Snider measured a result within 1% of the value predicted by gravitational time dilation. [36] (See Pound–Rebka experiment) In 2010, gravitational time dilation was measured at the Earth's surface with a height difference of only one meter, using optical atomic clocks. [26]
In the Schwarzschild solution, it is assumed that the larger mass M is stationary and it alone determines the gravitational field (i.e., the geometry of space-time) and, hence, the lesser mass m follows a geodesic path through that fixed space-time. This is a reasonable approximation for photons and the orbit of Mercury, which is roughly 6 ...
The measured elapsed time of a light signal in a gravitational field is longer than it would be without the field, and for moderate-strength nearly static fields the difference is directly proportional to the classical gravitational potential, precisely as given by standard gravitational time dilation formulas.
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 ...
where the numerator is the gravitational, and the denominator is the kinematic component of the time dilation. For a particle falling in from infinity the left factor equals the right factor, since the in-falling velocity v {\textstyle v} matches the escape velocity c r s r {\textstyle c{\sqrt {\frac {r_{\text{s}}}{r}}}} in this case.