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 N_c; ^\(\epsilon\)_m; C₀; ∆N_c; 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.

1. Time evolution is computed (with the initial state shown in eq. (35)) for many different values of the parameter C_m 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=N_c and X=K, respectively. Subsequently, "rewriting values" of C_m are selected as those for which the amplitude of n₀ is sufficiently large (1.2 times than in the case C_m=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).
2. 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 C_m around rewriting value of C_m for C₀=0.01. Next, Mathematica-notebooks with the names "_New.nb" or "_NewRates.nb" are used to select around each rewriting value the C_m 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).