AI 中文总结
该研究通过磁恩斯特反演构建并分析稳态轴对称真空度规，探讨克尔 - 纽特几何结构及曼科 - 鲁伊斯参数\(C\)和扭转常数\(\beta\)的作用，给出相关条件和准则，通过计算得到多种结果，如零点范围、不变量极限等，确定了视界位置和渐近形式。
AI 中文摘要
我们构建并分析了通过对具有曼科 - 鲁伊斯参数\(C\)和反演前扭转常数\(\beta\)的克尔 - 纽特进行磁恩斯特反演得到的稳态轴对称真空度规。该变换处于埃勒斯轨道；我们的贡献在于依赖纽特的几何结构以及\(C\)和\(\beta\)在其轴、视界、奇点和方位角 - 因果性结构中的作用。反演在正则域上保持规范外尔半径、带符号的WLP分子\(F\)以及\(g_{\phi\phi}\)的符号。在选定极点\(x = \sigma\)处，\(C = -\sigma\)，局部轴条件和锥度由\(\chi_\sigma^{(\beta)}=\beta - 2m(2\sigma a + 3l)\)控制。所选种子恩斯特代表的外部零点服从精确准则\(-\beta\in\mathcal{R}_C\)；对于采样族，数值轨迹产生具有封闭形式角端点的半直线范围。对于\(D = a^2 + l^2 - 2alC\neq0\)，\(\Lambda_\beta\Sigma\)有一个有限非零的种子环极限。高精度计算发现沿采样射线二次外尔不变量的与方向无关的有限极限，但未确定\(C^2\)可扩展性。在\(\beta = 0\)时，对于采样的\(C = -1,0\)情况发现外部简单恩斯特零点，而\(C = +1\)时未发现，这与计算范围一致。在一个零点附近，克雷奇曼标量有一般的六阶爆炸；数值角度扫描确定了低阶的特殊方向。正则（\(g_{\phi\phi}>0\)）外部的所有采样点都是佩特罗夫I型。候选视界位置仍然是克尔 - 纽特的，渐近形式是列维 - 奇维塔型。
英文摘要
We construct and analyze stationary, axisymmetric vacuum metrics obtained by magnetic Ernst inversion of Kerr-NUT with Manko-Ruiz parameter $C$ and pre-inversion twist constant $β$. The transformation lies in the Ehlers orbit; our contribution is the NUT-dependent geometry and the roles of $C$ and $β$ in its axis, horizon, singularity, and azimuthal-CTC structure. The inversion preserves the canonical Weyl radius, the signed WLP numerator $F$, and the sign of $g_{ϕϕ}$ on regular domains. At the selected pole $x=σ$, $C=-σ$, the local axis condition and conicity are controlled by $χ_σ^{(β)}=β-2m(2σa+3l)$. Exterior zeros of the chosen seed Ernst representative obey the exact criterion $-β\in\mathcal{R}_C$; for the sampled families numerical traces yield half-line ranges with closed-form corner endpoints. For $D=a^2+l^2-2alC\ne0$, $Λ_βΣ$ has a finite nonzero seed-ring limit. High-precision calculations find direction-independent finite limits of both quadratic Weyl invariants along the sampled rays, without establishing $C^2$-extendibility. At $β=0$, exterior simple Ernst zeros are found for the sampled $C=-1,0$ cases but not for $C=+1$, consistently with the computed ranges. Near one zero the Kretschmann scalar has a generic sixth-order blow-up; a numerical angular scan identifies exceptional directions of lower order. All sampled points in the regular ($g_{ϕϕ}>0$) exterior are Petrov type I. Candidate horizon locations remain those of Kerr-NUT, and the asymptotics are Levi-Civita type.
Commentsv2: refs added; v1: 26 pages, 2 figures, 1 table
