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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 ...
In the Schwarzschild solution, it is assumed that the larger mass M is stationary and it alone determines the gravitational field (i.e., the geometry of space-time) and, hence, the lesser mass m follows a geodesic path through that fixed space-time. This is a reasonable approximation for photons and the orbit of Mercury, which is roughly 6 ...
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.
Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2 × 10 −4 sec when the radar pulses pass near the sun. Such a change, equivalent to 60 km in distance, could now be measured over the required path ...
where c is the speed of light, and Δr and Δt denote differences of the space and time coordinates, respectively, between the events. The choice of signs for s 2 above follows the space-like convention (−+++). A notation like Δr 2 means (Δr) 2. The reason s 2 and not s is called the interval is that s 2 can be positive, zero or negative.
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 ...
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Time dilation refers to the expansion or contraction in the rate at which time passes, and was the subject of the Gravity Probe A experiment. Under Einstein's theory of general relativity, matter distorts the surrounding spacetime. This distortion causes time to pass more slowly in the vicinity of a massive object, compared to the rate ...