Why does time run slower near a black hole?

Why does time run slower near a black hole?

Time dilation

General relativity is Einstein's Theory of gravity, in General relativity the proper time of the observer for Schwarzschild black hole is given by

$ d\tau ^2 = ( 1 - \frac{2GM}{r})dt^2 + ( 1 - \frac{2GM}{r})^{-1} dr^2 + r^2 d\Omega ^2$

Where $d \Omega ^2 = d \theta ^2 + \sin^{2}\theta d\phi^2$

Here $ d\tau $ is proper time of an observer that means it's time what observer's clock reads

Now consider that our observer is not having any motion in space that is $dr = d\phi = d\theta = 0$ so our equation now becomes

$ d\tau^2 = ( 1 - \frac{2GM}{r})dt^2 $

$ d\tau = (1 - \frac{2GM}{r})dt  ...(1) $

But what does dt means in eq(1)? 

if your observer is far away from the gravitating object then we can take 

$  r \approx \infty $ then

$ d\tau  = dt $,

 so $ dt$ is time experienced by observer who is really far away from the object or dt is time experienced by observer who is in flat spacetime.

if observer is out side the even horizon $(r > 2GM)$ then $ d\tau < dt $. 

So this is what it means when you say that your time runs slower near the blackhole.