AI 中文总结
研究对一些弱场外尔共形引力解进行批判性分析，指出前人用二阶泊松方程生成解有误，应使用四阶方程，还指出这些度规推导存在其他不一致，如用已知CG（电）真空解描述物质分布内部是错误的。
AI 中文摘要
共形引力（CG）的场方程由度规的四阶导数构建。广义相对论（GR）的二阶场方程在弱场极限下简化为二阶泊松方程，而CG的场方程则产生一个四阶方程。尽管如此，Tanhayi、Fathi和Takook等人的工作在弱场极限下使用二阶泊松方程来生成所谓的CG解。我们证明，由于使用了二阶泊松方程而非合适的四阶方程，这些解是错误的。我们还指出了这些度规推导中的其他不一致之处，比如声称已知的CG（电）真空解描述了物质分布的内部。
英文摘要
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.
CommentsAdded 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
