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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 ...
The post-Newtonian expansion is a calculational method that provides a series of ever more accurate solutions to a given problem. [12] The method is iterative; an initial solution for particle motions is used to calculate the gravitational fields; from these derived fields, new particle motions can be calculated, from which even more accurate ...
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 faster the relative velocity, the greater the time dilation between them, with time slowing to a stop as one clock approaches the speed of light (299,792,458 m/s). In theory, time dilation would make it possible for passengers in a fast-moving vehicle to advance into the future in a short period of their own time.
Bending of waves in a gravitational field. Due to gravity, time passes more slowly at the bottom than at the top, causing the wave-fronts (shown in black) to gradually bend downwards. The green arrow shows the direction of the apparent "gravitational attraction". The orbital equation can be derived from the Hamilton–Jacobi equation. [15]
The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential equation given initial conditions. In the context of general relativity , it means the problem of finding solutions to Einstein's field equations — a system of hyperbolic partial differential equations — given some initial ...
Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks, [67] while ongoing validation is provided as a side effect of the operation of the Global Positioning System (GPS). [68] Tests in stronger gravitational fields are provided by the observation of binary pulsars. [69]
Since the light would be slowed down by gravitational time dilation (as seen by outside observer), the regions with lower gravitational potential would act like a medium with higher refractive index causing light to deflect. This reasoning allowed Einstein in 1911 to reproduce the incorrect Newtonian value for the deflection of light. [41]