论文标题
Bona-Masso切片条件和接近黑洞穿刺的失误
Bona-Masso slicing conditions and the lapse close to black-hole punctures
论文作者
论文摘要
我们考虑了几个功能系列$ f（α）$，这些家族出现在Bona-Masso切片条件下，$α$。专注于球形对称和与时间无关的切片，我们将这些条件应用于Schwarzschild时空，以便在Areal Radius $ r $方面构建lapse $α$的分析表达式。然后，我们转换为各向同性坐标，并确定$α$在黑洞穿刺附近的各向同性半径$ r $上的依赖性。我们提出了先前考虑的功能$ f（α）$的概括，为此，在领导订单中，失误与$ r $而不是$ r $ $ r $的非全能功率成正比。我们还在球形对称性中执行动力学模拟，并在使用光谱方法的数值模拟中证明了上述选择的优势。
We consider several families of functions $f(α)$ that appear in the Bona-Masso slicing condition for the lapse function $α$. Focusing on spherically symmetric and time-independent slices we apply these conditions to the Schwarzschild spacetime in order to construct analytical expressions for the lapse $α$ in terms of the areal radius $R$. We then transform to isotropic coordinates and determine the dependence of $α$ on the isotropic radius $r$ in the vicinity of the black-hole puncture. We propose generalizations of previously considered functions $f(α)$ for which, to leading order, the lapse is proportional to $r$ rather than a non-integer power of $r$. We also perform dynamical simulations in spherical symmetry and demonstrate advantages of the above choices in numerical simulations employing spectral methods.
