{"paper":{"title":"On the Buchdahl inequality for spherically symmetric static shells","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Hakan Andreasson","submitted_at":"2006-05-17T10:41:29Z","abstract_excerpt":"A classical result by Buchdahl \\cite{Bu1} shows that for static solutions of the spherically symmetric Einstein-matter system, the total ADM mass M and the area radius R of the boundary of the body, obey the inequality $2M/R\\leq 8/9.$ The proof of this inequality rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl's hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in $[R_0,R_1], R_0>0,$ of matter models for which the energy density $\\rho\\geq 0,$ and the radial- a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0605097","kind":"arxiv","version":2},"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"}