Numerical data for "Black Hole Metamorphosis and Stabilization by Memory Burden [arXiv:2006.00011]"

This is the numerical data that belongs to the paper G. Dvali, L. Eisemann, M. Michel, S. Zell, Black Hole Metamorphosis and Stabilization by Memory Burden, Phys. Rev. D 102 (2020) 103523, arXiv:2006.00011. The numerical data is generated using the computer program TimeEvolver, which was presented in M. Michel, S. Zell, TimeEvolver: A Program for Time Evolution With Improved Error Bound, Comput. Phys. Commun. 277 (2022) 108374, arXiv:2205.15346. In the following, equation numbers refer to the latest arXiv-version of arXiv:2006.00011, where also all relevant definitions can be found. In this paper, the procedure for generating the data, which we summarize in the following, is also described in more detail. First, among the five parameters Nc; \(\epsilon\)m; C0; ∆Nc; K all but one are fixed (according to eq. (36)). Then for different values of the remaining unfixed parameter - subsequently called X - the following 2-step process is performed. Time evolution is computed (with the initial state shown in eq. (35)) for many different values of the parameter Cm in the interval [0;1] (sampling step 10-3). The results for X are stored in five folders called "X", the subfolders of which contain data for different values of X. For example, the subfolder "01" of the folder "C0" consists of data for C0=0.01. Please note that the folders "Cgap", "N0" and "Q" correspond to X=\(\epsilon\)m, X=Nc and X=K, respectively. Subsequently, "rewriting values" of Cm are selected as those for which the amplitude of n0 is sufficiently large (1.2 times than in the case Cm=0). This is done in Mathematica-notebooks "_New.nb". Finally, rewriting values for different values of X are collected using Mathematica-notebooks with names that start on "_Meta". These notebooks generate the 5 plots shown in figures 4(a), 5(a), 6(a), 7(a) and 8(a). Next finer scans are performed around some of the rewriting values determined in step 1 (new sampling step 5 10-5). The results are stored in five folders called "XRates", where again subfolders correspond to different values of X. For example, the subfolder "01" of the folder "C0Rates" consists of finer scans in Cm around rewriting value of Cm for C0=0.01. Next, Mathematica-notebooks with the names "_New.nb" or "_NewRates.nb" are used to select around each rewriting value the Cm that leads to the largest rate (see definition in arXiv:2006.00011). Finally, these maximal rates for different values of X are collected using Mathematica-notebooks with names that start on "_Meta" and end on "Rates.nb". These notebooks generate the 5 plots shown in figures 4(b), 5(b), 6(b), 7(b) and 8(b).

本数据集隶属于论文G. Dvali、L. Eisemann、M. Michel、S. Zell所著的《Black Hole Metamorphosis and Stabilization by Memory Burden》，发表于《Phys. Rev. D》102 (2020) 103523，预印本编号arXiv:2006.00011。本数据集的数值结果由计算机程序TimeEvolver生成，该程序见于M. Michel、S. Zell的《TimeEvolver: A Program for Time Evolution With Improved Error Bound》，发表于《Comput. Phys. Commun.》277 (2022) 108374，预印本编号arXiv:2205.15346。下文提及的方程编号均以arXiv:2006.00011的最新预印本版本为准，该版本中也包含所有相关定义。本文中，我们将在下文简要总结的数据生成流程，也有更详细的阐述。首先，在参数$N_c$、$epsilon_m$、$C_0$、$Delta N_c$、$K$中，固定其中四个参数（依据式(36)），随后针对剩余的未固定参数（后续记为$X$）的不同取值，执行如下两步流程。第一步为时间演化计算：以式(35)给出的初始态为基准，对区间$[0,1]$内的参数$C_m$的多个不同取值进行计算（采样步长为$10^{-3}$）。针对$X$的计算结果被存储于五个名为"X"的文件夹中，其子文件夹对应不同$X$的取值数据。例如，文件夹"C0"下的子文件夹"01"对应$C_0=0.01$的数据集。请注意，文件夹"Cgap"、"N0"、"Q"分别对应$X=epsilon_m$、$X=N_c$、$X=K$的场景。随后，在Mathematica笔记本"_New.nb"中，选取满足$n_0$振幅足够大（为$C_m=0$时的1.2倍）的$C_m$"重写取值"。针对不同$X$的重写取值，通过名称以"_Meta"开头的Mathematica笔记本进行汇总，此类笔记本可生成图4(a)、5(a)、6(a)、7(a)与8(a)所示的5幅绘图。接下来，针对第一步中确定的部分重写取值，执行更精细的参数扫描（新的采样步长为$5 imes10^{-5}$）。其结果被存储于五个名为"XRates"的文件夹中，其子文件夹同样对应不同$X$的取值。例如，文件夹"C0Rates"下的子文件夹"01"对应$C_0=0.01$时，围绕$C_m$重写取值的精细扫描数据。随后，通过名称为"_New.nb"或"_NewRates.nb"的Mathematica笔记本，在每个重写取值附近选取可获得最大速率的$C_m$（相关定义详见arXiv:2006.00011）。最终，通过名称以"_Meta"开头且以"Rates.nb"结尾的Mathematica笔记本，汇总不同$X$对应的最大速率数据，此类笔记本可生成图4(b)、5(b)、6(b)、7(b)与8(b)所示的5幅绘图。