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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 ...
Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of ...
In general relativity, the Einstein–Rosen metric is an exact solution to the Einstein field equations derived in 1937 by Albert Einstein and Nathan Rosen. [1] It is the first exact solution to describe the propagation of a gravitational wave.
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;
According to general relativity, in its weak-field and low-velocity linearized approximation, a slowly spinning body induces an additional component of the gravitational field that acts on a freely-falling test particle with a non-central, gravitomagnetic Lorentz-like force.
In particular, the direction of motion with respect to the sense of rotation of the central body is relevant because co-and counter-propagating waves carry a "gravitomagnetic" time delay Δt GM which could be, in principle, be measured [2] [3] if S is known.
This equation has two solutions: = (). These concentric event horizons become degenerate for 2 r Q = r s , which corresponds to an extremal black hole . Black holes with 2 r Q > r s cannot exist in nature because if the charge is greater than the mass there can be no physical event horizon (the term under the square root becomes negative). [ 9 ]
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.