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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 new class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential. Space, in this construction, still has the ordinary Euclidean geometry. However, spacetime as
The geometry of general curved surfaces was developed in the early 19th century by Carl Friedrich Gauss. This geometry had in turn been generalized to higher-dimensional spaces in Riemannian geometry introduced by Bernhard Riemann in the 1850s. With the help of Riemannian geometry, Einstein formulated a geometric description of gravity in which ...
The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. In general relativity, the metric tensor plays the role of the gravitational potential in the classical theory of gravitation, although the physical ...
In Einstein's theory of relativity, the path of an object moving relative to a particular frame of reference is defined by four coordinate functions x μ (τ), where μ is a spacetime index which takes the value 0 for the timelike component, and 1, 2, 3 for the spacelike coordinates.
For a clock traveling at 0.3 c, the elapsed time measured by the observer is 5.24 meters (1.75 × 10 −8 s), while for a clock traveling at 0.7 c, the elapsed time measured by the observer is 7.00 meters (2.34 × 10 −8 s). [3]: 220–221 This illustrates the phenomenon known as time dilation. Clocks that travel faster take longer (in the ...
The metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the Einstein field equations). Using the weak-field approximation , the metric tensor can also be thought of as representing the 'gravitational potential'.
Diagram regarding the confirmation of gravitomagnetism by Gravity Probe B. Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity.