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On the accuracy of the IWM-CFC approximation in differentially rotating relativistic stars. (English) Zbl 1305.83030
Summary: 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.
MSC:
83C15 Exact solutions to problems in general relativity and gravitational theory
85A15 Galactic and stellar structure
83-08 Computational methods for problems pertaining to relativity and gravitational theory
53Z05 Applications of differential geometry to physics
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