论文标题
非线性统计样条小样条型，用于关键球形黑洞解决方案4维
Nonlinear Statistical Spline Smoothers for Critical Spherical Black Hole Solutions in 4-dimension
论文作者
论文摘要
本文着重于爱因斯坦的自相似重力崩溃解决方案 - 轴 - 二析配置，用于SL（2，r）转换的两个共轭类别。这些溶液在时空扩张下是不变的，结合了内部变换。在爱因斯坦 - 轴 - 迪拉顿文献中，我们首次应用了非线性统计样条回归方法来估计四个维度的关键球形黑洞溶液。这些样条方法包括截短的功率基础，天然立方样条和受惩罚的B型单频。平均而言，统计模型的预测错误几乎小于$ 10^{-2} $，因此所有开发的模型都可以视为无偏见的估计器，用于整个域上关键崩溃功能。除了这一卓越之外，我们还为所有关键崩溃功能得出了封闭形式和不断可区分的估计器。
This paper focuses on self-similar gravitational collapse solutions of the Einstein--axion-dilaton configuration for two conjugacy classes of SL(2, R) transformations. These solutions are invariant under spacetime dilation, combined with internal transformations. For the first time in Einstein--axion-dilaton literature, we apply the nonlinear statistical spline regression methods to estimate the critical spherical black hole solutions in four dimension. These spline methods include truncated power basis, natural cubic spline and penalized B-spline. The prediction errors of the statistical models, on average, are almost less than $10^{-2}$, so all the developed models can be considered unbiased estimators for the critical collapse functions over their entire domains. In addition to this excellence, we derived closed forms and continuously differentiable estimators for all the critical collapse functions.
