  We determine the accuracy of the conformal flatness (IWM-CFC) approximation
for the case of single, but strongly differentially rotating relativistic
stars. We find that for the fastest rotating and most relativistic polytropic
models, the deviation from full general relativity is below 5% for integrated
quantities and below 10% for local quantities, such as the angular velocity.
Furthermore, we study the deviation of the IWM-CFC approximation from full
general relativity by evaluating and comparing different error indicators. We
find that for the models that are not near the maximum mass, a simple error
indicator constructed from local values of the metric potentials is more
indicative of the accuracy of the IWM-CFC approximation than an error indicator
that is based on the Cotton-York tensor. Furthermore, we construct a simple,
linear empirical relation that allows for the estimation of the error made by
the IWM-CFC approximation and which only involves the flattening of the star
due to rotation and the minimum value of the lapse function. Thus, in any
numerical simulation involving rotating relativistic stars, one can readily
know the deviations from full general relativity due to the IWM-CFC
approximation.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena