The IWM-CFC approximation in differentially rotating relativistic stars

Many astrophysically relevant systems have been studied, in recent years, by means of the spatial conformal flatness condition (IWM-CFC), yielding very satisfactory results as far as the accuracy of IWM-CFC approximation is concerned. Here, we determine the accuracy of IWM-CFC for the case of single, but strongly differentially rotating stars, modeled by a polytropic equation of state. We find that for the fastest rotating models, the deviation from full general relativity is still below 2% for most integrated quantities and reaches up to 6% for sensitive quantities, such as the angular velocity at the equator. We construct a simple error indicator and demonstrate that it correlates well with the largest errors observed in physical quantities characterizing the model.