2. Let us consider Hanging Observer (HO), standing in one place in "r" distance to source of gravity. HO is useful, because any body traveling through space, may be considered as body passing spots where such observers stands. At least we, on Earth, are such HOs.
We denote HO proper time following Schwarzschild metric as:
So, we will denote above ratio as:
3. We may now express Schwarzschild metric relative to such HO observers' proper-times as:
4. So now, let us check geodesic for photon relative to proper time of HO it passes. For every HO we have: