{"paper":{"title":"Ambiguity in matter sector for modified gravity involving $\\delta^2 \\mathcal{L}_{m}/\\delta g^{\\mu\\nu}\\delta g^{\\alpha\\beta}$ and its implications to astrophysics and cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE"],"primary_cat":"gr-qc","authors_text":"A. Sulaksono, B. N. Jayawiguna","submitted_at":"2026-08-05T13:59:14Z","abstract_excerpt":"Matter density ($\\rho$) and radial pressure ($p$) are often used as the matter Lagrangian density ($\\mathcal{L}_{m}$) because both are thermodynamically consistent and produce the same Einstein field equation (EFE) in general relativity (GR). New gravity models with explicit links between matter and geometry instead involve second-order derivatives of $\\mathcal{L}_{m}$ relative to the metric tensor. So, picking either $p$ or $-\\rho$ for $\\mathcal{L}_{m}$ gives different effective EFEs. This confusion appears because one usually treats the four-velocity ($u_\\mu$) and the metric tensor ($g_{\\mu "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04867","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04867/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"}