AI 中文总结
研究具有 NUT 荷时空的黑洞状态空间确定问题，引入双视界扇区诊断方法，通过调和平均关系确定温度，分析 Taub - NUT 的扇区闭合情况，发现 NUT 参数进入方式及二级毛发定义，旋转 Kerr - NUT 母体隐藏共形对称性可作一致性检验。
AI 中文摘要
具有 NUT 荷的时空有几种不等价的热力学表述，它们各自遵循自己的第一定律和 Smarr 关系，仅宏观一致性并不能确定黑洞状态空间。我们引入一种双视界扇区诊断方法，其温度由调和平均关系确定而非作为势来调整。对于不带电的 Taub - NUT，和扇区在质量与 NUT 荷下闭合，而差扇区在此处测试的受限均匀诊断类中，仅在包含类似旋转的热力学二级毛发\(J_n = mn\)后才闭合。因此，在这种扇区诊断中，NUT 参数通过\(N = n\)和均匀组合\(J_n = mn\)进入。二级毛发在均匀质量表示中脱壳定义，而非作为新的度规参数或渐近荷。旋转 Kerr - NUT 母体的隐藏共形对称性给出了一致性检验，无需假设全息对偶。
英文摘要
After decades without a fully self-consistent thermodynamic formulation, recent proposals for Lorentzian Taub-NUT spacetime have yielded several inequivalent descriptions, each satisfying its own first law and Smarr relation, leaving unresolved which formulation is physically preferred. In this Letter we introduce a two-horizon diagnostic whose sector temperatures are fixed by harmonic mean relations before the thermodynamic variables are chosen. For uncharged Taub-NUT, the sum sector closes with the mass and NUT charge, whereas, within the restricted homogeneous class examined here, the difference sector requires the thermodynamic secondary hair $J_n=mn$. This result supports a bi-hair thermodynamic organization of the NUT parameter through $N=n$ and $J_n=mn$. Furthermore, this two-horizon framework offers a new route toward addressing similar thermodynamic nonuniqueness in other two-horizon systems when the first law and Smarr relation alone do not identify a physically preferred formulation.
Comments7 pages
