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Title of Journal: Gen Relativ Gravit

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Abbravation: General Relativity and Gravitation

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Springer US

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1572-9532

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On the accuracy of the IWM–CFC approximation in di

Authors: Panagiotis Iosif Nikolaos Stergioulas
Publish Date: 2014/09/17
Volume: 46, Issue: 10, Pages: 1800-
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Abstract

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 approximationWe are grateful to Andi Bauswein for useful discussions This work was supported by an IKY–DAAD exchange grant IKYDA 2012 and a Virgo EGO Scientific Forum VESF fellowship for doctoral studies by the European Gravitational Observatory EGODIR1262012/EGODIR802013 Partial support also provided by “NewCompStar” COST Action MP1304

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