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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 ...
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;
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.
Solutions are also used to describe the motion of binary stars around each other, and estimate their gradual loss of energy through gravitational radiation. General relativity describes the gravitational field by curved space-time; the field equations governing this curvature are nonlinear and therefore difficult to solve in a closed form.
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 sources of any gravitational field (matter and energy) is represented in relativity by a type (0, 2) symmetric tensor called the energy–momentum tensor. It is closely related to the Ricci tensor. Being a second rank tensor in four dimensions, the energy–momentum tensor may be viewed as a 4 by 4 matrix.
Relation between the speed and the Lorentz factor γ (and hence the time dilation of moving clocks). Time dilation as predicted by special relativity is often verified by means of particle lifetime experiments. According to special relativity, the rate of a clock C traveling between two synchronized laboratory clocks A and B, as seen by a ...
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.