标题： Kerr Taub-NUT Ads黑洞的第一定律 显示英文标题

标题： First Law for Kerr Taub-NUT AdS Black Holes

摘要： 黑洞力学的第一定律，即能量的变化与熵和其他守恒荷的变化之间的关系，一直是探测黑洞热力学性质的主要动机。 在这项工作中，我们研究了Kerr Taub-NUT AdS黑洞的热力学性质。 我们提出了黑洞荷的几何Komar定义，这些定义按构造满足Smarr公式。 此外，基于欧拉定理的尺度论证，我们建立了Kerr Taub-NUT AdS黑洞的第一定律。 相应的一般化第一定律包括宇宙常数、NUT荷和角动量的变化。 构建中的关键新要素是两个角动量、黑洞和Misner弦角动量的独立变化。 利用Brown-York准局域荷定义，我们表明我们关于质量和自旋的表达式与广义的 Komar表达式一致。 我们指出这些结果对于旋转AdS黑洞的热力学的重要性，包括选择正确的类时Killing矢量以产生正确的热力学质量。 显示英文摘要

摘要： The first law of black hole mechanics, which relates the change of energy to the change of entropy and other conserved charges, has been the main motivation for probing the thermodynamic properties of black holes. In this work, we investigate the thermodynamics of Kerr Taub-NUT AdS black holes. We present geometric Komar definitions for the black hole charges, that by construction satisfy the Smarr formula. Further, by a scaling argument based on Euler's theorem, we establish the first law for the Kerr Taub-NUT AdS black holes. The corresponding first law includes variations in the cosmological constant, NUT charges and angular momenta. The key new ingredient in the construction are the independent variations of both angular momenta, the black hole and Misner string angular momenta. Employing the Brown-York quasilocal charge definitions we show that our expression for the mass and spin coincide with our generalized Komar expressions. We indicate the relevance of these results to the thermodynamics of rotating AdS black holes, including the proper choice of time-like Killing vector to produce the correct thermodynamic mass.