{"paper":{"title":"Dynamics of nonlinear scalar field with Robin boundary condition on the Schwarzschild--Anti-de Sitter background","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AP"],"primary_cat":"gr-qc","authors_text":"Filip Ficek, Maciej Maliborski","submitted_at":"2023-12-05T13:40:18Z","abstract_excerpt":"This work concerns the dynamics of conformal cubic scalar field on a Schwarzschild--anti-de Sitter background. The main focus is on understanding how it depends on the size of the black hole and the Robin boundary condition. We identify a critical curve in the parameter space that separates regions with distinct asymptotic behaviours. For defocusing nonlinearity, the global attractor undergoes a pitchfork bifurcation, whereas for the focusing case, we identify a region of the phase space where all solutions blow up in finite time. In the course of this study we observe an interplay between bla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.02760","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/2312.02760/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"}