The IWM–CFC approximation in differentially rotating relativistic stars

Abstract

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.