According to Wikipedia, the gravitational time dilation formula is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}}[/tex]

where

t0 is the proper time between events A and B for a slow-ticking observer within the gravitational field,

tf is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate),

and r is the radial coordinate of the observer.

Does this mean that if we get arbitrarily close to the event horizon we can make our time dilation factor increase arbitrarily without bound? Does this also mean that for an observer on the event horizon time never passes?

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# Gravitational time dilation at the event horizon

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