Exceptional lines in the Kerr-Newman black hole spectrum

Datasets associated with the article Exceptional lines in the Kerr-Newman black hole spectrum. The file Kerr-Newman Results.zip is organized into four main directories: Data and Analytic Expression, Data for Exceptional Lines, Paths Gamma_1,2,3 for Kerr-Newman BH, and Scripts in Julia. Each folder includes its own set of subfiles together with a README file detailing their contents. A brief description of each folder is given below: Kerr-Newman Results.zip Data and Analytic Expression Folder "Data and Analytic Expression" contains a Mathematica notebook that performs the derivation of the asymptotic expansion for the frequency of Zero-Damping Modes (ZDMs) evaluated at the extremal limit. To support and validate this analytic derivation, the folder also includes three text files containing numerical data obtained using the isomonodromic method. These datasets are used to generate the verification plot shown in Figure 6 (also added to the folder, namely 'Fig. 6 - ZDMs_Analytic_Expression.pdf' of the associated work, where the analytic expression is directly compared against the numerical results. Folder Data for Exceptional Lines Folder "Data for Exceptional Lines" presents numerical data for the exceptional lines (ELs) for the mode (ℓ, m) = (1, 1) in the parameter space of Kerr-Newman black holes. The data track the evolution of exceptional points (EPs) from the Kerr limit to the massless perturbation regime in Kerr-Newman black holes. Together with the data, this folder contains Figures 1, 3, and 4, which provide visual representations of the exceptional lines and their behavior in the parameter space, along with the branching in the spectrum into zero-damping modes and damped modes. Folder Paths Gamma_1,2,3 for Kerr-Newman BH Folder "Paths Gamma_1,2,3 for Kerr-Newman BH" contains the data associated with the trajectories Gamma_1, Gamma_2, and Gamma_3 shown in Figures 2 and 3. The figures are also available in the folder entitled: Spectral_Permutation.pdf and Plot_3D_for_path_Gamma_2_Re(ω).pdf. For each trajectory, data are provided for both directions: Clockwise orientation / Counterclockwise orientation. These trajectories are defined in the parameter space and are used to investigate the behavior of the modes around the first two EPs in the Kerr-Newman spectrum for (ℓ, m) = (1, 1). Folder Scripts in Julia Folder contains Julia scripts used for the analysis of exceptional lines (ELs) in Kerr-Newman black hole perturbations going from non-extremal M^2 < a^2 + Q^2 to extremal M^2 = a^2 + Q^2. 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.