 This gives us

In this coordinate system, an observer at radial position "r" sees a vector positioned at "r" as rotating with angular frequency ω.This observer, however, sees a vector positioned at some other value of "r" as rotating at a different rate, due to relativistic time dilation.Transforming the Schwarzschild metric into the rotating frame, and assuming that formula_4 is a constant, we find

with formula_6.