{"paper":{"title":"Exact gravitational potential of a homogeneous torus in toroidal coordinates and a surface integral approach to Poisson's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","gr-qc"],"primary_cat":"physics.class-ph","authors_text":"Matt Majic","submitted_at":"2018-02-28T01:28:32Z","abstract_excerpt":"New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to Poisson's equation plus some solution to Laplace's equation. The full solutions are then obtained using two equivalent methods, applying differential boundary conditions at the surface, or evaluating a surface integral derived from Green's third identity. This surface integral may not have been published before and is general to all geometries and volume den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00003","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":""},"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"}