AI 中文总结
本文研究爱因斯坦-高斯-博内 AdS 引力中洛伦兹 Taub-NUT 时空的热力学，通过离壳形式计算温度、能量和熵，提出包含 NUT 参数独立变化的全余维第一定律，并给出高斯-博内修正。
AI 中文摘要
我们研究了任意偶数维爱因斯坦-高斯-博内 AdS 引力中洛伦兹 Taub-NUT 时空的热力学，这些时空被构造为爱因斯坦-凯勒底流形上的 $U(1)$ 纤维丛。我们利用表面引力计算温度，并使用离壳 Abbott-Deser-Tekin 形式将能量作为与稳态 Killing 矢量相关的守恒荷。在同一框架内，我们将熵作为视界 Noether 荷获得。该结果与 Iyer-Wald 公式一致，并包含对 Bekenstein-Hawking 面积定律的高斯-博内修正。只要存在 Misner 弦，我们就保留它们，并制定一个全余维第一定律，其中 NUT 参数独立于视界半径变化。这需要额外的热力学荷及其共轭势，我们明确确定了它们。我们还简要讨论了静态极限。
英文摘要
We study the thermodynamics of Lorentzian Taub--NUT spacetimes in Einstein--Gauss--Bonnet AdS gravity in arbitrary even dimensions, constructed as $U(1)$ fibrations over Einstein--Kähler base manifolds. We compute the temperature from the surface gravity and the energy as the conserved charge associated with the stationary Killing vector using the off-shell Abbott--Deser--Tekin formalism. Within the same framework, we obtain the entropy as a horizon Noether charge. The result agrees with the Iyer--Wald formula and includes a Gauss--Bonnet correction to the Bekenstein--Hawking area law. Retaining the Misner strings whenever present, we formulate a first law of full cohomogeneity in which the NUT parameter varies independently of the horizon radius. This requires an additional thermodynamic charge and its conjugate potential, which we determine explicitly. We also briefly discuss the static limit.
Commentsv1: 20 pages, v2: Format changed. References added
