AI 中文总结
研究具有非最小耦合的高维标量-张量理论中精确球对称解，通过主方程形式体系推导广义费希尔-贾尼斯-纽曼-维尼康尔（FJNW）和伊尔马兹-罗森度规的耦合函数及标量场势关系，揭示不同情况下的引力特性。
AI 中文摘要
本文研究具有非最小耦合的高维标量-张量引力理论，着重于精确球对称解的重构。系统应用先前工作中发展的形式体系，该体系表明任何静态球对称度规都可表示为具有特定耦合函数$f(\phi)$和势$U(\phi)$的标量-张量理论的精确解。分析聚焦于任意时空维度中的两类重要解：费希尔-贾尼斯-纽曼-维尼康尔（FJNW）度规及其极限情况广义伊尔马兹-罗森度规。利用约旦框架中的主方程形式体系，推导了这两类解族的耦合函数$f(\phi)$和标量场势$U(\phi)$的关键关系。对于FJNW度规，在$s = 2$，$D = 6$的特殊情况下，耦合函数$f(\phi)$在$u^3 > M$的区域为正，对应引力吸引且势$U(\phi) = 0$的规范标量场。相比之下，对于任意维度$D > 4$的广义伊尔马兹-罗森度规，重构的耦合函数始终为负，$f(\phi) < 0$，表明具有负动能和斥力引力的幻标量场。
英文摘要
This paper investigates higher-dimensional scalar-tensor theories of gravity with nonminimal coupling, focusing on the reconstruction of exact spherically symmetric solutions. We systematically apply the formalism developed in previous works, which demonstrates that any static spherically symmetric metric can be represented as an exact solution of a scalar-tensor theory with specific coupling functions $f(ϕ)$ and potential $U(ϕ)$. Our analysis centers on two important classes of solutions in arbitrary spacetime dimensions: the Fisher-Janis-Newman-Winicour (FJNW) metric and its limiting case, the generalized Yilmaz-Rosen metric. We derive the key relations for the coupling function $f(ϕ)$ and the scalar field potential $U(ϕ)$ for both solution families using the master equation formalism in the Jordan frame. For the FJNW metric, we find that in the special case $s = 2$, $D = 6$, the coupling function $f(ϕ)$ is positive in the domain $u^3 > M$, corresponding to gravitational attraction and a canonical scalar field with vanishing potential $U(ϕ) = 0$. In contrast, for the generalized Yilmaz-Rosen metric in arbitrary dimensions $D > 4$, the reconstructed coupling function is always negative, $f(ϕ) < 0$, indicating a phantom scalar field with negative kinetic energy and repulsive gravity.
Comments23 pages, 2 figures
