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How does gravity affects time? Expression of relation between time and gravityi

Hi Srijan,

The answer to your question can be very involved, and I'm not sure how mathematical you'd like the answer.

For now, time is dilated (compressed) outside a non-rotating spherical mass according to the relation:

to = tf * sqrt (1 - 2 * G * M / (r * c ^ 2) ) = tf * sqrt ( 1 - rs / r )

to 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),
G is the gravitational constant,
M is the mass of the object creating the gravitational field,
r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),
c is the speed of light, and
rs is the Schwarzschild radius of M.

This is a consequence of General Relativity.

At the Schwarzschild radius of a Black Hole, to = O, or no time passes at all!

But perhaps the best non-mathematical explanation of gravitational time dilation is given by

Hope that helps.

Prof. James Gort  


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James Gort


Questions on observational astronomy, optics, and astrophysics. Specializing in the evolution of stars, variable stars, supernovae, neuton stars/pulsars, black holes, quasars, and cosmology.


I was a professional astronomer (University of Texas, McDonald Observatory), lecturer at the Adler Planetarium, professor of astrophysics, and amateur astronomer for 42 years. I have made numerous telescopes, and I am currently building one of the largest private observatories in Canada.

StarDate, University of Texas, numerous Journal Publications

B.A. Physics and Astronomy M.Sc. Physics Ph.D. Astrophysics

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