In a recent study, Wei et al. (2024) [96] proposed a universal classification scheme that interprets black hole solutions, including the four-dimensional Schwarzschild, Reissner-Nordström (RN), Schwarzschild-AdS, and RN-AdS black hole solutions, as topological defects within the thermodynamic parameter space, and then divides black hole solutions into four distinct classes, denoted as W1−, W0+, W0−, and W1+, offering insights into deeper aspects of black hole thermodynamics and gravity. In this paper, we investigate the universal thermodynamic topological classification of the singly rotating Kerr black holes in all dimensions, as well as the four-dimensional Kerr-Newman black hole. We show that the innermost small black hole states of the d≥6 singly rotating Kerr black holes are thermodynamically unstable, while those of the four-dimensional Kerr-Newman black hole and the d=4,5 singly rotating Kerr black holes are thermodynamically stable. On the other hand, the outermost large black holes exhibit unstable behavior in all these cases. At the low-temperature limit, the d≥6 singly rotating Kerr black holes have one large thermodynamically unstable black hole state, while the four-dimensional Kerr-Newman black hole and the d=4,5 singly rotating Kerr black holes feature one large unstable branch and one small stable branch. Conversely, at the high-temperature limit, the d≥6 singly rotating Kerr black holes exhibit a small unstable black hole state, while the four-dimensional Kerr-Newman black hole and the d=4,5 singly rotating Kerr black holes have no black hole states at all. Consequently, we demonstrate that the d≥6 singly rotating Kerr black holes belong to the class W1−, whereas the four-dimensional Kerr-Newman and d=4,5 singly rotating Kerr black holes belong to the class W0+, thereby further support the conjecture proposed in Wei et al. (2024) [96].

中文翻译：

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旋转黑洞的通用热力学拓扑类别


在最近的一项研究中，Wei et al. （2024） [96] 提出了一种通用分类方案，将黑洞解决方案（包括四维 Schwarzschild、Reissner-Nordström （RN）、Schwarzschild-AdS 和 RN-AdS 黑洞解决方案）解释为热力学参数空间内的拓扑缺陷，然后将黑洞解决方案分为四个不同的类别，分别表示为 W1−、W0+、W0− 和 W1+， 提供对黑洞热力学和引力更深层次的见解。在本文中，我们研究了单向旋转的 Kerr 黑洞在所有维度上以及四维 Kerr-Newman 黑洞的通用热力学拓扑分类。我们表明，d≥6 单旋克尔黑洞的最内层小黑洞状态在热力学上是不稳定的，而四维克尔-纽曼黑洞和 d=4,5 单旋克尔黑洞的黑洞状态在热力学上是稳定的。另一方面，在所有这些情况下，最外层的大黑洞都表现出不稳定的行为。在低温极限下，d≥6 单旋克尔黑洞具有一个大的热力学不稳定黑洞状态，而四维克尔-纽曼黑洞和 d=4,5 单旋克尔黑洞具有一个大的不稳定分支和一个小的稳定分支。相反，在高温极限下，d≥6 个单旋的克尔黑洞表现出一个小的不稳定黑洞状态，而四维的克尔-纽曼黑洞和 d=4,5 个单旋的克尔黑洞根本没有黑洞态。 因此，我们证明了 d≥6 个单旋转的克尔黑洞属于 W1− 类，而四维的 Kerr-Newman 和 d=4,5 个单旋转的克尔黑洞属于 W0+ 类，从而进一步支持了 Wei et al. （2024） [96] 提出的猜想。