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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 ...
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.
More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation. [64] Gravitational redshift has been measured in the laboratory [65] and using astronomical observations. [66] Gravitational time dilation in the Earth's gravitational ...
The coordinate time is the time that would be read on a hypothetical "coordinate clock" situated infinitely far from all gravitational masses (=), and stationary in the system of coordinates (=). The exact relation between the rate of proper time and the rate of coordinate time for a clock with a radial component of velocity is:
For example, in a system composed of one planet orbiting a star, the motion of the planet is determined by solving the field equations with the energy–momentum tensor the sum of that for the planet and the star. The gravitational field of the planet affects the total spacetime geometry and hence the motion of objects. It is therefore ...
Gravitational time dilation: Clocks run slower in deeper gravitational wells. [11] Precession: Orbits precess in a way unexpected in Newton's theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars). Light deflection: Rays of light bend in the presence of a gravitational field.
This curvature gives rise to the gravitational force. A common analogy is placing a heavy object on a stretched out rubber sheet, causing the sheet to bend downward. This curves the coordinate system around the object, much like an object in the universe curves the coordinate system it sits in.
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.