High-order WKB with Padé approximants and Cesàro means enables computation of black-hole overtones and long-lived quasinormal modes, with a noted limitation that apparent convergence can be incorrect for some metrics.
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First-order eikonal formulas connect a scalarized black-hole metric to quasinormal modes, shadows, strong lensing, and grey-body factors via photon-sphere invariants in the weak-hair limit.
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Ces\`aro convergence of the high-order WKB method and its applications to black-hole overtones and long-lived modes
High-order WKB with Padé approximants and Cesàro means enables computation of black-hole overtones and long-lived quasinormal modes, with a noted limitation that apparent convergence can be incorrect for some metrics.
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A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
First-order eikonal formulas connect a scalarized black-hole metric to quasinormal modes, shadows, strong lensing, and grey-body factors via photon-sphere invariants in the weak-hair limit.