I'm just curious, is there a way to calculate the speed of light in a gravitational field? From my understanding, light travels slower in a gravitational field and the speed is zero in a black hole. Is there an equation to determine the speed of light on earth (not including slowing down due to air) compared to the speed of light in a vacuum? The closest I could find was this which says that c'=co(1 + V/c^2)
where V is the potential energy - GMm/r
At the schwarzschild radius, r=2GM/c^2, the speed of light would be 0.5c. However, we know that the speed of light in a black hole is zero. Am I missing something here?