{"paper":{"title":"Odd-parity perturbations of trace-quadratic $f(R,T)$ black holes with anisotropic matter: admissible branches, axial ringdown, and a coupled-PINN benchmark","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Adnan Malik, Ahdab K. Althukair, M. Farasat Shamir, Mushtaq Ahmad","submitted_at":"2026-06-02T12:32:49Z","abstract_excerpt":"We study odd-parity gravitational perturbations of static black holes in trace-quadratic $f(R,T)=R+\\alpha T^2$ gravity supported by an anisotropic effective fluid with constant closure parameters $(w_r,w_t)$. From the unreduced axial system and its principal symbol, we identify the sector of parameter space that supports a regular horizon, asymptotic flatness, and hyperbolic odd-sector evolution. Within this closure the admissible branch lies at negative $w_r$, while the commonly used positive-$w_r$ family fails the background regularity test and is kept only as a numerical comparison branch. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06517","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/2606.06517/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"}