旋转大黄蜂真空解的轴向阻碍
Axial Obstructions to Rotating Bumblebee Vacuum Solutions
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中文总结 AI 辅助
研究正则旋转常范数矢量真空的阻碍，通过分析极点处对称性及沿轴锥度变化对曲率的影响，应用于爱因斯坦 - 大黄蜂引力中克尔 - 变形解，发现其矢量真空在轴上不光滑且极轴有奇点，特殊分支有正则外视界及局部旋转解。
中文摘要 AI 辅助
我们确定了正则旋转常范数矢量真空的两个一般阻碍。首先，在非退化分岔面的极点处，视界和轴向不变性迫使每个继承对称性的光滑一元形式消失，这与严格非零的常范数相矛盾。其次，我们表明沿旋转轴变化的锥度会产生奇异曲率，该曲率随着到轴的逆固有距离而发散。我们将这些结果应用于爱因斯坦 - 大黄蜂引力中的一般三参数族克尔 - 变形解。因此，由于非零常范数，其矢量真空在轴上不光滑，并且位置依赖的锥度导致极轴上出现真正的曲率奇点。然而，一个特殊的非极值分支在远离轴的地方允许一个正则的外 Killing 视界，并在非极区域定义了一个精确的局部旋转解。
英文摘要
We establish two obstructions to globally regular rotating constant-norm vector vacua. At an axial fixed point of a regular nondegenerate bifurcate Killing horizon, horizon-boost and axial invariance force every smooth symmetry-inheriting one-form to vanish, contradicting a strictly nonzero constant norm. Independently, varying axial conicity produces an orthonormal curvature component diverging as the inverse proper distance and precludes a \(C^2\) extension. Applied to a three-parameter Kerr--disformal family in Einstein--bumblebee gravity, these results reveal a nonsmooth bumblebee one-form, while direct calculation shows that the Kretschmann scalar diverges as the inverse square of the transverse proper distance to either open exterior axis. Even the distinguished nonextremal branch selected by nonpolar outer-horizon regularity is therefore an exact nonpolar rotating exterior solution, not a globally regular isolated black hole. Together, these field- and metric-level obstructions provide a two-pronged no-go framework for globally regular rotating constant-norm vector vacua.
