{
  "abstract": "We develop a harmonic framework for spherically symmetric Friedmann-like geometries with constant scalar curvature but non-zero trace-free Ricci curvature. This preserves Friedmann-type isotropic expansion while introducing a radially varying tidal field and supporting anisotropic stress. We formulate the scalar Laplace-Beltrami operator as a Sturm-Liouville problem and establish its self-adjoint domains and regularity at minimal spheres. Robertson-Walker harmonics are recovered in the maximally symmetric limit. Trace-free curvature terms are expressed as spectral projection kernels. Rotational symmetry preserves angular labels and parity, while the tidal profile couples different radial eigenmodes. A finite-shell calculation displays this off-diagonal structure, verifies consistency between radial representations, and confirms the expected weak-field scaling. A minimally coupled scalar field remains diagonal in the exact basis, indicating operator-dependent mixing rather than mixing solely due to inhomogeneity. We formulate transverse-traceless kernels, whose dynamical application requires a specified model for the supporting anisotropic matter. This converts curvature-induced mode mixing into a spectral problem for perturbations beyond maximally symmetric cosmologies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20199",
  "author_total": 4,
  "authors": [
    {
      "name": "Eduardo Bittencourt"
    },
    {
      "name": "Peter K. S. Dunsby"
    },
    {
      "name": "Bob Osano"
    },
    {
      "name": "Muzikayise E. Sikhonde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j4ffgds1tnwj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20199",
  "fulltext_url": null,
  "id": "1j4ffgds1tnwj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20199",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7221879898",
  "pdf_url": "https://arxiv.org/pdf/2610.20199",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j4ffgds1tnwj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.20199",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20199"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies",
  "title_text": "Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/1j4ffgds1tnwj",
  "venue": "arXiv",
  "versions": []
}