非最小耦合 $Y(R)F^2$ 引力中标量场与各向异性物质的黑洞解

中文摘要 AI 辅助

我们研究了非最小耦合的爱因斯坦-麦克斯韦理论中精确的球对称静态黑洞解，该理论属于 $Y(R)F^2$ 类型，并扩展了一个最小耦合的实标量场和各向异性物质分布。麦克斯韦场通过 Ricci 标量的任意函数与时空曲率耦合，而标量场则由动能项和标量势描述。我们针对非最小耦合函数的幂律和对数形式获得了精确解，并分析了相应的时空几何。特别地，我们识别出一个特殊的 $\eta=-1/3$ 情形，在此情形下一般的幂律解变得奇异，并通过独立求解场方程推导出一个新的对数度规。所得构型是渐近平坦的，并展现出与标量场、各向异性物质和非最小电磁耦合之间相互作用相关的修正引力性质。我们进一步证明，磁解通过电磁对偶变换可得到带电对应解，在该变换下度规和标量扇区保持不变，而非最小耦合函数被反转。所得解为在曲率依赖的电磁理论中研究黑洞视界、热力学性质、测地线运动以及星系旋转曲线等天体物理现象提供了有用的框架。

英文摘要

We investigate exact spherically symmetric and static black hole solutions in a non-minimally coupled Einstein--Maxwell theory of the $Y(R)F^2$ type, extended by a minimally coupled real scalar field and an anisotropic matter distribution. The Maxwell field is coupled to the spacetime curvature through an arbitrary function of the Ricci scalar, while the scalar field is described by a kinetic term and a scalar potential. We obtain exact solutions for power-law and logarithmic forms of the non-minimal coupling function and analyze the corresponding spacetime geometries. In particular, we identify a special $β=-1/3$ case for which the general power-law solution becomes singular and derive a new logarithmic metric by solving the field equations independently. The resulting configurations are asymptotically flat and exhibit modified gravitational properties associated with the interplay between the scalar field, anisotropic matter, and non-minimal electromagnetic coupling. We further show that the magnetic solutions admit electrically charged counterparts through an electromagnetic duality transformation, under which the metric and scalar sector remain invariant while the non-minimal coupling function is inverted. The obtained solutions provide a useful framework for investigating black hole horizons, thermodynamic properties, geodesic motion, and astrophysical phenomena such as galactic rotation curves in curvature-dependent electromagnetic theories.

发表机构

• Pamukkale University（帕穆克卡莱大学）

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39 pages