{"paper":{"title":"Dynamic Aspects of Bumblebee Gravity: Post-Newtonian Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Bumblebee gravity's PPN framework is self-consistent up to 1.5PN order only when the Bumblebee field couples directly to the Einstein tensor.","cross_cats":["hep-ph"],"primary_cat":"gr-qc","authors_text":"Hao Li, Jie Zhu","submitted_at":"2026-05-17T16:00:11Z","abstract_excerpt":"In this work, we investigate the dynamic aspects of Bumblebee gravity via the parameterized post-Newtonian method. We find that the PPN framework is self-consistent up to 1.5PN order if and only if $\\lambda = -\\xi/2$, which corresponds to a direct coupling between the Bumblebee field $B_\\mu$ and the Einstein tensor. The requirement of tachyonic stability restricts the Bumblebee potential to satisfy $V''(0)=0$. In the specific case where $\\lambda = -\\xi/2$, the resulting PPN metric yields non-vanishing values for the parameters $\\alpha_1$ and $\\alpha_2$, as well as a novel PPN potential $U_B$ t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The PPN framework is self-consistent up to 1.5PN order if and only if λ = −ξ/2, which corresponds to a direct coupling between the Bumblebee field B_μ and the Einstein tensor.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes the standard PPN coordinate system and expansion remain valid for the Bumblebee vector field without additional higher-order or non-perturbative corrections from the potential.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Bumblebee gravity is self-consistent in PPN up to 1.5PN order only for λ = −ξ/2, producing non-zero α1, α2, a logarithmic U_B potential, and a pulsar-timing bound |ℓ| ≲ 1.6×10^{-9}.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Bumblebee gravity's PPN framework is self-consistent up to 1.5PN order only when the Bumblebee field couples directly to the Einstein tensor.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b48d4c6549a38de3eabe458a39e968975efd6ce3a345a65516e94090bf929bd3"},"source":{"id":"2605.17516","kind":"arxiv","version":1},"verdict":{"id":"3265b433-1ef2-4c68-a1df-503b1f0c29bd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:08:23.179978Z","strongest_claim":"The PPN framework is self-consistent up to 1.5PN order if and only if λ = −ξ/2, which corresponds to a direct coupling between the Bumblebee field B_μ and the Einstein tensor.","one_line_summary":"Bumblebee gravity is self-consistent in PPN up to 1.5PN order only for λ = −ξ/2, producing non-zero α1, α2, a logarithmic U_B potential, and a pulsar-timing bound |ℓ| ≲ 1.6×10^{-9}.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes the standard PPN coordinate system and expansion remain valid for the Bumblebee vector field without additional higher-order or non-perturbative corrections from the potential.","pith_extraction_headline":"Bumblebee gravity's PPN framework is self-consistent up to 1.5PN order only when the Bumblebee field couples directly to the Einstein tensor."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17516/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:19.865398Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:20:55.419026Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.649791Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.627484Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"03031ef74fe0b00d972585146cdc003f400446f68f1035a03d5761b56e25bd11"},"references":{"count":39,"sample":[{"doi":"","year":1989,"title":"V. A. Kostelecky and S. Samuel, Spontaneous Breaking of Lorentz Symmetry in String Theory, Phys. Rev. D39, 683 (1989)","work_id":"303c93c0-6471-454f-98a6-95a1ff290512","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"D. Colladay and V. A. Kostelecky, CPT violation and the standard model, Phys. Rev. D55, 6760 (1997), arXiv:hep- ph/9703464","work_id":"61f0c044-3d01-4775-b2d3-9ab1655e2843","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"Lorentz-violating extensio n of the standard model","work_id":"c595f262-4018-4a25-a97f-42132c3b15ad","ref_index":3,"cited_arxiv_id":"hep-ph/9809521","is_internal_anchor":true},{"doi":"","year":2001,"title":"D. Colladay and V. A. Kostelecky, Cross-sections and Lorentz violation, Phys. Lett. B511, 209 (2001), arXiv:hep- ph/0104300","work_id":"c5cfdd45-0229-4257-b13c-db7005fb79df","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2001,"title":"Stability, causality, and Lorentz and CPT violation","work_id":"791fe98b-80a2-49e8-8855-8409616a76c8","ref_index":5,"cited_arxiv_id":"hep-th/0012060","is_internal_anchor":true}],"resolved_work":39,"snapshot_sha256":"2c0e852b988c4cd542c79bc83b02709b390344e342e446a516af07414ccd6535","internal_anchors":12},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5f920383a2b7ae15c55efd9c628f203c1a0dac3d5e465817a517f1e33cbde3b6"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}