Critical analysis of some weak-field Weyl conformal gravity solutions

[2607.20381] Critical analysis of some weak-field Weyl conformal gravity solutions Skip to main content Search Submit Donate Log in General Relativity and Quantum Cosmology arXiv:2607.20381 (gr-qc) [Submitted on 22 Jul 2026 ( v1 ), last revised 22 Aug 2026 (this version, v2)] Title: Critical analysis of some weak-field Weyl conformal gravity solutions Authors: Miguel Yulo Asuncion , Reinosuke Kusano View PDF HTML (experimental) Abstract: The field equations of Conformal Gravity (CG) are constructed from fourth-order derivatives of the metric. While the second-order field equations of General Relativity (GR) reduce to a second-order Poisson equation in the weak-field limit, those of CG yield a fourth-order one. Despite this, works by Tanhayi, Fathi, and Takook [Mod. Phys. Lett. A 26, 2403 (2011)], Payandeh and Fathi [Int. J. Th. Phys. 51, 2227 (2012)], and Fathi, Olivares, and Villanueva [Galaxies 9, 43 (2021)] use second-order Poisson equations to generate purported solutions to CG in a weak-field limit. We demonstrate that these solutions are erroneous due to the use of second-order Poisson equations instead of appropriate fourth-order ones. We also point out other inconsistencies in the derivations of these metrics, such as the assertion that known CG (electro)vacuum solutions describe the interiors of matter distributions. Comments: Added references to other papers that cite the studies being critiqued. Added a footnote on a correspondence between General Relativity and Conformal Gravity in vacuum (A)dS settings Subjects: General Relativity and Quantum Cosmology (gr-qc) ; High Energy Physics - Theory (hep-th) Cite as: arXiv:2607.20381 [gr-qc] (or arXiv:2607.20381v2 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2607.20381 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jesus Miguel Yulo Asuncion [ view email ] [v1] Wed, 22 Jul 2026 17:11:31 UTC (410 KB) [v2] Sat, 22 Aug 2026 17:13:34 UTC (73 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2026-07 Change to browse by: hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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