非线性电动力学中的高维缓慢旋转黑洞

中文摘要 AI 辅助

我们研究了任意时空维度 $d \geq 4$ 中缓慢旋转、非线性带电的黑洞，采用广义的 Lense--Thirring 拟设。在旋转参数的一阶线性近似下，我们求解了爱因斯坦-非线性电动力学（NLE）场方程，针对依赖于单一不变量的受限理论 ${\cal L}({\cal S})$。我们推广了 arXiv:2203.01919 中证明的四维“No Go 定理”，并证明了在 $d \geq 4$ 中麦克斯韦理论的唯一性。与四维情况类似，我们证明了标准的旋转生成技巧无法为任何非平凡的 NLE 理论在高维中产生完整的旋转解。我们识别出一族 NLE 理论，它们允许缓慢旋转的解，其矢量势以类似麦克斯韦的方式编码旋转效应；在四维中，这重现了先前发现的 RegMax 理论，而在 $d\geq4$ 中，我们以闭式形式获得了相应的电势，并以径向坐标的函数隐式地给出了相关的拉格朗日量。

英文摘要

We study slowly rotating, nonlinearly charged black holes in arbitrary spacetime dimension $d \geq 4$, using a generalized Lense--Thirring ansatz. Working to linear order in the rotation parameters, we solve the Einstein--nonlinear electrodynamics (NLE) field equations for restricted theories ${\cal L}({\cal S})$ depending on single invariant. We provide an extension of the four-dimensional "No Go theorem" proven in ArXiv:2203.01919 and demonstrate the uniqueness of Maxwell theory in $d \geq 4$. Similar to four dimensions, it is proven that the standard rotation generating trick fails to produce full rotating solutions for any nontrivial NLE in higher dimensions. We identify a family of NLE theories admitting slowly rotating solutions with vector potentials encoding rotation effect in Maxwell-like manner; in four dimensions this reproduces the previously found RegMax theory, while in $d\geq4$ we obtain the corresponding electric potential in closed form and the associated Lagrangian implicitly as a function of the radial coordinate.

发表机构

• Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）

机构由 AI 辅助整理，请以论文原文为准。