Data and scripts for: "Ergodic Hysteresis of the Kerr black hole spectrum"

Datasets associated with the article Ergodic Hysteresis of the Kerr black hole spectrum - Phys. Rev. D 113, L101504 (arXiv: 2511.16640 [gr-qc]). The file Isomonodromy Results.zip is organized into two main directories: Kerr Black Hole and Extremal Kerr Black Hole.Each directory includes its own set of subfolders together with a README file detailing their contents. A brief description of each subfolder is given below: Isomonodromy Results.zip Folder Kerr Black Hole Subfolder "Adiabatic Paths l2m2" contains numerical data for radial eigenvalues (quasinormal frequencies) and angular eigenvalues as functions of the scalar-field mass and the Kerr spin. These values were computed along the closed adiabatic path ABCDEFA, which begins and ends at the Schwarzschild limit (a/M, Mμ) = (0, 0). Along this path, we track the adiabatic evolution of the fundamental Schwarzschild mode with (ℓ, m) = (2, 2). Subfolder "Data for Surface n=3" contains data obtained using the isomonodromic method. The datasets include QNMs as functions of both the scalar-field mass and the Kerr black hole spin, for the n = 3 overtone surface. Subfolder "DMs - ZDMs" contains data covering the degeneracy cascade for the mode (ℓ, m) = (1, 1). This includes the transition between Damped Modes (DMs) and Zero-Damped Modes (ZDMs). Subfolder "Eigenvalue difference near EP" provides numerical values associated with the local behavior of QNM eigenvalues near exceptional points of massive scalar perturbations of Kerr black holes. Note: We have added to the folder "Adiabatic Paths l2m2" an archive named "FA_n=26_l=m=2_via_Continued_Fraction.csv" that contains additional data for the segment FA for the n=26 mode. This archive complements the FA_n=26_l2m2_Mµ_0.0_a_0.99_to_0.0.txt archive. Folder Extremal Kerr Black Hole Subfolder "DMs Results + Script" contains 5 files in the formats .txt, .jl, and .pdf, all related to the computation of quasinormal modes of scalar perturbations in extremal Kerr black holes using the isomonodromic method. The findqnm_Extremal_KerrBH.jl script implements the QNM computation, using the Fredholm determinant representation of the Painlevé III τ-function, and allows exploration of the interval (Mμ)_∗^c < Mμ < (Mμ)_max. This script has been tested with Julia 1.10.7 LTS and ArbNumerics 1.5.3. It is currently NOT compatible with Julia 1.11.X, likely due to changes in memory allocation breaking compatibility with libArb. Note: The data in this repository extends the analysis previously presented in the papers “Exceptional point and hysteresis in perturbations of Kerr black holes” and “Massive scalar perturbations in Kerr black holes: near-extremal analysis”, available at the Zenodo record https://doi.org/10.5281/zenodo.13961216. Published in Phys. Rev. D 113, L101504 – 28 May, 2026 DOI: https://doi.org/10.1103/mssm-ws7d