论文标题
重新访问黑洞的热力学拓扑
Revisiting thermodynamic topologies of black holes
论文作者
论文摘要
在广义的非壳自由能景观中，黑洞可以视为热力学拓扑缺陷。时空的局部拓扑特性可以由缺陷处的绕组数反映出，而全球拓扑性质可以按拓扑数进行分类，拓扑数是所有局部绕组数的总和。我们建议可以通过隔离的单阶极点的残基来计算绕组数，该残基由外壳自由能构成的表征功能的特征函数。使用残基方法，我们表明黑洞的拓扑结构可以分为三类，拓扑数分别为-1、0和1，与[Phys中获得的结果一致。莱特牧师。 129，191101（2022）]使用拓扑电流方法。此外，我们指出，标准缺陷点，产生和an灭点以及临界点可以通过在这些单数点处的非壳特征表征功能的laurent系列的系数来区分。
In the generalized off-shell free energy landscape, black holes can be treated as thermodynamic topological defects. The local topological properties of the spacetime can be reflected by the winding numbers at the defects, while the global topological nature can be classified by the topological number which is the sum of all local winding numbers. We propose that the winding numbers can be calculated via the residues of isolated one-order pole points of characterized functions constructed from the off-shell free energy. Using the residue method, we show that the topologies of black holes can be divided into three classes with the topological numbers being -1, 0, and 1, respectively, being consistent with the results obtained in [Phys. Rev. Lett. 129, 191101 (2022)] by using the topological current method. Moreover, we point out that standard defect points, generation and annihilation points, and critical points can be distinguished by coefficients of the Laurent series of the off-shell characterized function at those singular points.
