关于差分旋转相对论星中IWM-CFC近似的精度
On the accuracy of the IWM-CFC approximation in differentially rotating relativistic stars
摘要：
我们确定的保形平坦度（IWM-CFC）近似的情况下，单一的，但强烈差分旋转相对论性恒星的准确性。我们发现，对于最快的旋转和相对论性最强的多方模型，与完整的广义相对论的偏差是低于5%的整体量和低于10%的本地量，如角速度。此外，我们还通过评估和比较不同的误差指标，研究了IWM-CFC近似与完全广义相对论的偏差。我们发现，对于不接近最大质量的模型，一个简单的误差指标构造的度量电位的局部值是更指示的IWM-CFC近似的准确性比一个错误的指标，是基于科顿约克张量。此外，我们构建了一个简单的，线性的经验关系，允许估计的误差由IWM-CFC近似，它只涉及扁平的恒星由于旋转和最小值的失效函数。因此，在任何涉及旋转相对论性恒星的数值模拟中，人们都可以很容易地知道由于IWM-CFC近似而导致的与完全广义相对论的偏差。
英文摘要：
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.
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