Main Question or Discussion Point
In this Wiki link for the derivation of the Schwarzschild metric, in the section "simplifying the components", g_22 and g_33 are derived. The problem is that upon deriving them, they first set those local measurements of the components for the metric upon a 2_sphere (on the left side) equal to measurements made by a distant observer (on the right side), rather than between two local observers as they claim. Since these components are the tangent distance, this automatically sets tangent distances the same for all static observers, not actually derived as far as I can tell, since it is originally supposed to only be between two local observers. From what I can see, all we can really say about the measurements of two local observers upon the 2-sphere is that since they are angle and rotation independent, is that g_22 and g_33 will both carry the same co-efficient, but we have not determined what that co-effient is yet, so we cannot just automatically assume it to be unity for all static observers, right? What am I missing or is there something missing in the link?