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Gravitational Time Dilation

This effect has been experimentally verified and is crucial for GPS functionality.

📜

The statement of the theorem

For a stationary clock at a radial distance

r

from a mass

M

in a weak gravitational field, the relationship between the proper time

d\tau

measured by the clock and the coordinate time

dt

measured by an observer far away (

r \to \infty

) is derived from the metric component

g_{00}

:\n

\frac{d\tau}{dt} = \sqrt{-g_{00}} \approx \sqrt{1 - \frac{2GM}{rc^2}}

\nThis shows that the rate of time passage decreases as the gravitational potential increases (i.e., as

r

decreases).

Source: Wikipedia