# Is gravitational time dilation the same for an object at $x$ radii from a black hole no matter what size the black hole is?

Assuming you have two non-rotating black holes. Black hole 1 is 1 meter in radius while black hole 2 is 10 meters in radius.

If you are standing 10 meters from black hole 1, would you experience the same time dilation effects as someone standing 100 meters from black hole 2?

Based on math I have done I believe the answer is yes, but I would like to know what other people think and see how they do their math.

• What math have you done? This might help us tailor an answer that's appropriate to your level
– Jim
Commented Mar 30, 2015 at 23:36
• physics.stackexchange.com/questions/158212/…
– Joe
Commented Mar 30, 2015 at 23:37
The radius of a black hole, the Schwarzschild radius, is proportional to the mass of the black hole: $$r=\frac{2GM}{c^2} \to r \propto M$$ Therefore, a black hole with a larger radius must have a greater mass. So black hole #2 is ten times as massive as black hole #1.
The formula for gravitational time dilation is $$\frac{t_0}{t_f} = \sqrt{1- \frac{2GM}{rc^2}}$$ Black hole #2 has ten times the mass of black hole #1, and you're standing ten times as far away from black hole #2 as you are from black hole #1.