{"paper":{"title":"FLRW spaces as submanifolds of $\\mathbb{R}^6$: restriction to the Klein-Gordon operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"A. Belokogne, E. Huguet, J. P. Arias Zapata, J. Queva, J. Renaud","submitted_at":"2017-11-29T11:07:43Z","abstract_excerpt":"The FLRW spacetimes can be realized as submanifolds of $\\mathbb{R}^6$. In this paper we relate the Laplace-Beltrami operator for an homogeneous scalar field $\\phi$ of $\\mathbb{R}^6$ to its explicit restriction on FLRW spacetimes. We then make the link between the homogeneous solutions of the equation $\\square_6 \\phi = 0$ in $\\mathbb{R}^6$ and those of the Klein-Gordon equation $(\\square_{f} - \\xi R^f + m^2)\\phi^f=0 $ for the free field $\\phi^f$ in the FLRW spacetime. We obtain as a byproduct a formula for the Ricci scalar of the FRLW spacetime in terms of the function $f$ defining this spaceti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10771","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"}