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I am trying to understand in practice the Gravitational Time Dilation by calculating the time distortion near the supermassive black hole Sgr A* in our Galactic Center.

According to Einstein's Theory of General Relativity, the time distortion near a black hole is calculated with the following formula:

T^2 = t^2 / 1 - ( Rs / r ), where:

T= Observer A time, far away from the black hole

t = Observer B close to the black hole

r = Distance between the black hole and Observer B

Rs= Schwarzschild Radius

For the Sgr A* black hole I found that the Schwarzschild Radius is Rs=13 * 10^16 km. Based on that, I tried to calculate how close to the Event Horizon of the black hole does Observer B have to be so that Observer A sees 60 seconds pass for every 12 seconds on Observer B clock. I calculated that the distance should be r=541.666,67 km

Could you tell me please if my reasoning is correct and if not what is the proper answer?

Thank you in advance!

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# I Gravitational time dilation calculation near a Black Hole

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