发表机构
Institute of Physics, University of the Philippines Los Baños（菲律宾大学洛斯巴尼奥斯分校物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究利用含高阶导数的非形式变换，确定了Klein-Gordon方程形式不变的最一般条件，发现二阶情形下存在保持传播解的非形式相关度规族，并将此类变换视为时空流形的形变。
AI 中文摘要
标量-张量理论通过引入标量场和度规张量来描述引力，从而扩展了广义相对论（GR）。尽管在广义相对论中物质部分与度规最小耦合，但标量场与物质的耦合可以通过非形式变换（Disformal Transformations）进行调整。由Takahashi、Motohashi和Minamitsuji提出的这些变换中最一般的一种，包含标量场的任意高阶导数，旨在将两个无鬼的高阶标量-张量理论相互映射。我们利用这些变换确定了标量场Klein-Gordon方程在非形式变换下保持形式不变的最一般条件。在二阶情形下，我们识别出一族非形式相关的度规，它们产生相同的传播解。此外，高阶情形在满足Klein-Gordon不变性的同时，也能符合理论和现象学约束。最后，我们探讨了将非形式变换视为时空流形“形变”的概念。
英文摘要
Scalar-Tensor theories extend General Relativity (GR) by including both a scalar field and a metric tensor in describing gravity. Although the matter sector is minimally coupled to the metric in GR, the scalar field coupling to matter may be adjusted by means of Disformal Transformations. One of the most general of these transformations, formulated by Takahashi, Motohashi, and Minamitsuji, include arbitrarily high-order derivatives of the scalar field and are designed to map between two ghost-free Higher-order Scalar-Tensor theories. We used these transformations to determine the most general conditions for the disformal form-invariance of the Klein-Gordon equation for the scalar field. In the second-order case, we identified a family of disformally-related metrics that result in the same propagation solutions. Additionally, higher-order cases could comply with theoretical and phenomenological constraints alongside KG-invariance. Finally, we investigated the notion of disformal transformations as ``deformations'' of the spacetime manifold.
Comments8 pages
