# Gravitational time dilation

## Main Question or Discussion Point

Hello,

I am trying to learn about Gravitational Time Dilation. I came across the following formula for time dilation in a uniform gravitational field:

$$T_d = {1-} \frac{gh}{c^{2}}}$$

but I cannot find any derivation for this. Can someone point me in the right direction?

Thanks

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cristo
Staff Emeritus
Take a look at http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

Now, the time dilation factor you state above is $$\sqrt{1-\frac{2gh}{c^2}$$ (It's equal to T0/T, in the above link).

Using the binomial theorem $$\sqrt{1+x}=1+\frac{1}{2x}+\cdots$$

And hence, we obtain the result above $$T_d=1-\frac{gh}{c^2}$$

Chris Hillman
cristo should have explained why we are supposed to take $2m/r = 2gh$ (in relativistic units in which G=c=1) in the Schwarzschild vacuum.