Published July 14, 2022 | Version v1
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Numerical data for "Black Hole Metamorphosis and Stabilization by Memory Burden [arXiv:2006.00011]"

  • 1. Ludwig-Maximilians-Universität München & Max-Planck-Institut für Physik
  • 2. Ben-Gurion University of the Negev
  • 3. École Polytechnique Fédérale de Lausanne


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.

  1. 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).
  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 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).


This work was supported in part, by the Humboldt Foundation under Humboldt Professorship Award, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy via the Munich Center for Quantum Science and Technology (EXC-2111 - 390814868) and the Excellence Cluster Origins (EXC-2094 - 390783311). The work of M.M. was supported by a Minerva Fellowship of the Minerva Stiftung Gesellschaft für die Forschung mbH, the Israel Science Foundation (grant No. 741/20) and by the Deutsche Forschungsgemeinschaft through a German-Israeli Project Cooperation (DIP) grant "Holography and the Swampland". The work of S.Z. was supported by ERC-AdG-2015 grant 694896.


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Is supplement to
Preprint: (URL)
Journal article: 10.1103/PhysRevD.102.103523 (DOI)


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