发表机构
China West Normal University; University of Waterloo（西华师范大学; 滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过双视界扇区诊断研究带电Kerr-Newman-NUT时空，发现Σ扇区由类电荷变量闭合，Δ扇区需类旋转变量，从而支持NUT双毛发结构：N为类电荷，J_N=MN为类旋转次级毛发。
AI 中文摘要
仅凭第一定律的一致性并不能确定带NUT荷时空的黑洞态空间，因为几种不等价的宏观表述都能产生一致的热力学。我们通过将内视界和外视界的熵及逆温度组织为和（Σ）与差（Δ）扇区，为带电的Kerr-Newman-NUT族开发了一种双视界扇区诊断方法。带电旋转几何对无电的Taub-NUT扇区结果提供了更严格的检验，因为质量M、普通电荷Q、普通角动量J、NUT荷N以及NUT次级毛发J_N=MN都进入相同的双视界热力学。对于本文定义并检验的物理锚定的最小齐次态空间，我们发现了清晰的扇区分离：Σ扇区由类电荷变量Q和N闭合，而Δ扇区还额外需要类旋转变量J和J_N。消除J_N或N的自然约化无法再现由扇区温度固定的第一定律系数，且它们相关的Bekenstein-Smarr关系在指定的标度权重下不闭合。在这一类中，电荷和普通旋转因此不能吸收NUT次级响应，带电旋转族支持NUT双毛发组织：N具有类电荷扇区角色，而J_N=MN是类旋转的热力学次级毛发。后者在齐次状态方程中离壳定义，而非作为新的度量参数或渐近守恒荷。
英文摘要
First law consistency alone does not determine the black hole state space of NUT-charged spacetimes, because several inequivalent macroscopic formulations can yield consistent thermodynamics. We develop a two-horizon sector diagnostic for the electrically charged Kerr-Newman-NUT family by organizing the inner- and outer-horizon entropies and inverse temperatures into sum ($Σ$) and difference ($Δ$) sectors. The charged rotating geometry gives a more stringent test of the uncharged Taub-NUT sector result, since the mass $M$, ordinary electric charge $Q$, ordinary angular momentum $J$, NUT charge $N$, and the NUT secondary hair $J_N=MN$ all enter the same two-horizon thermodynamics. For the physically anchored minimal homogeneous state spaces defined and tested here, we find a clear sector separation: the $Σ$ sector closes with the charge-like variables $Q$ and $N$, whereas the $Δ$ sector additionally requires the rotation-like variables $J$ and $J_N$. Natural reductions that eliminate either $J_N$ or $N$ fail to reproduce the first law coefficient fixed by the sector temperature, and their associated Bekenstein-Smarr relations do not close with the assigned scaling weights. Within this class, electric charge and ordinary rotation therefore do not absorb the NUT secondary response, and the charged rotating family supports the NUT bi-hair organization: $N$ has a charge-like sector role, while $J_N=MN$ is a rotation-like thermodynamic secondary hair. The latter is defined off shell in the homogeneous equation of state, not as a new metric parameter or asymptotic conserved charge.
Comments14 pages
