- #1
Jonsson
- 79
- 0
Hello there,
We know that for lightlike paths, there are circular geodesics at ##r = 3GM## in Schwarzschild geometry. Suppose an observer flashes his flashlight at ##r=3GM## and after some time the light reappears from the other side of the black hole. The time he measures is ##6 \pi GM##. I accidentally obtained this correct result, but I don't know why my method worked. I doubt it's a coincidence, and I'd like to understand why this is right. Basically by assuming that the light travels round a circle of length ##2\pi r## at a speed ##c = 1##. Write ##\Delta \tau = \frac{2 \pi r}{c} = 6 \pi GM ##
Why does this work? I expected this to only work using the coordinate time, i.e. i expected ## \Delta t = 6 \pi GM##, not ## \Delta \tau= 6 \pi GM##.
Thanks.
We know that for lightlike paths, there are circular geodesics at ##r = 3GM## in Schwarzschild geometry. Suppose an observer flashes his flashlight at ##r=3GM## and after some time the light reappears from the other side of the black hole. The time he measures is ##6 \pi GM##. I accidentally obtained this correct result, but I don't know why my method worked. I doubt it's a coincidence, and I'd like to understand why this is right. Basically by assuming that the light travels round a circle of length ##2\pi r## at a speed ##c = 1##. Write ##\Delta \tau = \frac{2 \pi r}{c} = 6 \pi GM ##
Why does this work? I expected this to only work using the coordinate time, i.e. i expected ## \Delta t = 6 \pi GM##, not ## \Delta \tau= 6 \pi GM##.
Thanks.