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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 ...
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
Gravitational time dilation near a large, slowly rotating, nearly spherical body, such as the Earth or Sun can be reasonably approximated as follows: [21] = where: t r is the elapsed time for an observer at radial coordinate r within the gravitational field;
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.
In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. The analogous solution for a charged, rotating body is given by the Kerr–Newman metric.
In 2010, Chou et al. performed tests in which both gravitational and velocity effects were measured at velocities and gravitational potentials much smaller than those used in the mountain-valley experiments of the 1970s. It was possible to confirm velocity time dilation at the 10 −16 level at speeds below 36 km/h. Also, gravitational time ...
Derivation of Newton's law of gravity Newtonian gravitation can be written as the theory of a scalar field, Φ , which is the gravitational potential in joules per kilogram of the gravitational field g = −∇Φ , see Gauss's law for gravity ∇ 2 Φ ( x → , t ) = 4 π G ρ ( x → , t ) {\displaystyle \nabla ^{2}\Phi \left({\vec {x}},t ...
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.