{"paper":{"title":"Ces\\`aro convergence of the high-order WKB method and its applications to black-hole overtones and long-lived modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Alexander Zhidenko, Jerzy Matyjasek, Roman A. Konoplya","submitted_at":"2026-05-25T11:03:23Z","abstract_excerpt":"We develop a fully automatic Mathematica implementation of the black-hole WKB method at very high orders based on the Bender-Wu algorithm, which in principle is limited only by memory and computational time, and show that when pushed to sufficiently high order and improved by diagonal Pad\\'e approximants the method becomes efficient for two regimes which are usually regarded as difficult for the standard low-order WKB treatment: the first several overtones with n>l and the very long-lived quasinormal modes of massive fields. At the same time, we show that this efficiency has a nontrivial limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25705","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25705/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}