标题： 黑洞极值和Davies型相变的拓扑解释 显示英文标题

标题： Topological interpretation of extremal and Davies-type phase transitions of black holes

摘要： 拓扑论证目前被用作一种新方法，以区分黑洞的特性，而忽略其详细结构和特定场方程。 在各种黑洞物理的研究途径中，这种新方法被广泛应用，其中黑洞热力学中的相变处于最前沿。 黑洞中有几种类型的相变，例如范德华型相变、戴维斯型相变、极端相变以及霍金-佩奇（HP）相变。 到目前为止，仅在不同时空中的范德华型相变和HP相变中获得了拓扑解释，其中临界点被识别为非零拓扑电荷。 为了完善这一图景，我们在此为另外两种相变提供相同的解释：戴维斯型相变和极端相变。 整个分析是普遍的，适用于观察到这些类型相变的任何时空。 更重要的是，我们的分析表明，在这些相变看似不同的情况下，它们具有相同的拓扑特征，\textit{即}从不同类型的相变中的不同热力学势中产生的非零拓扑电荷。 显示英文摘要

摘要： Topological arguments are currently being used as a novel scheme to discern the properties of black holes while ignoring their detailed structure and specific field equations. Among various avenues of black hole physics, where this novel approach is being utilized, the phase transition in black hole thermodynamics lies at the forefront. There are several types of phase transition in black holes; such as the van der Waals type phase transition, Davies-type phase transition, extremal phase transition, and Hawking-Page (HP) transition. So far, the topological interpretation, where the critical point has been identified with the non-zero topological charge, has been obtained only for the van der Waals type phase transition and HP transition in different spacetimes. To complete the picture, here we provide the same interpretation for two other phase transitions: Davies-type phase transition and extremal phase transition. The entire analysis is general and is valid for any spacetime where these types of phase transitions are observed. More importantly, our analysis suggests that amid the apparent differences in these phase transitions, they share the same topological characteristics, \textit{i.e.} non-zero topological charge arising from different thermodynamic potentials in different types of phase transition.