Say we have got a system in GR that is described by the Schwazschild metric. Then we perform a coordinate transform that gives the metric in a rotating system.
Why is the transformed metric not the Kerr metric in some form?
My suspicion is that this is due to the requirement that both Kerr and Schwarzschild metric tend to flat space far from the central mass. This assumption is used in the derivation of the two metrics. But why is this physical? And if what i have said so far is correct are there experimental tests of the "flatness" far from bodies that are assumed to be Schwarzschild/Kerr in our universe? (i.e. to test how useful these solutions to Einsteins equations are in modelling real objects).