{"paper":{"title":"Exact Toda Black Holes of Rank-2 Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"H. Lu, Peng-Yu Wu, Weicheng Zhao, Ze-Hua Wu","submitted_at":"2026-04-15T18:00:03Z","abstract_excerpt":"We consider Einstein gravity coupled to two Maxwell fields and one dilatonic scalar, and construct spherically-symmetric and static black holes that are charged under both Maxwell fields in general $D$ dimensions. We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. We devise a brute-force approach to obtain the most general but remarkably elegant solutions to the Toda equations. This allows us to construct exact black holes associated with all the rank-2 Lie groups. We study their thermodynamics and veri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. This allows us to construct exact black holes associated with all the rank-2 Lie groups. The B2 and G2 Toda black holes are new.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that suitable dilaton couplings exist such that the full system of Einstein-Maxwell-dilaton equations reduces exactly to Toda equations of rank-2 Lie groups without extra constraints or loss of generality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact spherically symmetric static black hole solutions are constructed for all rank-2 Lie groups by reducing Einstein-Maxwell-dilaton equations to Toda systems, with new B2 and G2 solutions, and thermodynamics derived without explicit metrics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a343450c9787ddcac3d936886c0b58c891f7765fffab7e7c69dddf48ef193aa9"},"source":{"id":"2604.14288","kind":"arxiv","version":2},"verdict":{"id":"377af23c-21d9-42c7-b03a-372d6cc82772","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T12:29:39.452116Z","strongest_claim":"We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. This allows us to construct exact black holes associated with all the rank-2 Lie groups. The B2 and G2 Toda black holes are new.","one_line_summary":"Exact spherically symmetric static black hole solutions are constructed for all rank-2 Lie groups by reducing Einstein-Maxwell-dilaton equations to Toda systems, with new B2 and G2 solutions, and thermodynamics derived without explicit metrics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that suitable dilaton couplings exist such that the full system of Einstein-Maxwell-dilaton equations reduces exactly to Toda equations of rank-2 Lie groups without extra constraints or loss of generality.","pith_extraction_headline":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.14288/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"}