标题： AdS空间中高斯-博内黑洞的拓扑性质 显示英文标题

标题： The topological natures of the Gauss-Bonnet black hole in AdS space

摘要： 在最近的提议[Phys. Rev. Lett. 129, 191101 (2022)]中，通过使用广义的非壳自由能，黑洞被视为拓扑热力学缺陷。在本文中，我们遵循这一提议来研究AdS空间中高斯-博内黑洞的局部和全局拓扑性质。局部拓扑性质由绕数反映，其中正的和负的绕数分别对应于稳定和不稳定的黑洞分支。全局拓扑性质由拓扑数反映，这些拓扑数定义为所有黑洞分支绕数的总和，可用于将黑洞分类到不同的类别中。当存在电荷时，我们发现拓扑数与参数的值无关，带电的高斯-博内AdS黑洞可以被分为具有相同拓扑数1的RNAdS黑洞的同一类。然而，当没有电荷时，我们发现拓扑数具有一定的维数依赖性。这与以前的研究不同，在以前的研究中，拓扑数被发现是一个与黑洞参数无关的普遍数值。此外，曲线{\tau }(r_h)在小半径和大半径极限下的渐近行为可以作为区分不同拓扑数的简单标准。 我们发现黑洞系统中存在一种新的渐近行为，当{\tau }(r_h \to 0) = 0 和{\tau }(r_h \to \infty ) = 0 时，这表明与渐近行为{\tau }(r_h \to 0)=\infty 和{\tau }(r_h \to \infty )=\infty 具有拓扑等价性。 我们还给出一个直观的证明，说明在条件 (\partial _{r_h} S)P > 0 下，黑洞系统为何只有三种拓扑类。 显示英文摘要

摘要： In the recent proposal [Phys. Rev. Lett. 129, 191101 (2022)], the black holes were viewed as topological thermodynamic defects by using the generalized off-shell free energy. In this paper, we follow such proposal to study the local and global topological natures of the Gauss-Bonnet black holes in AdS space. The local topological natures are reflected by the winding numbers, where the positive and negative winding numbers correspond to the stable and unstable black hole branches. The global topological natures are reflected by the topological numbers, which are defined as the sum of the winding numbers for all black hole branches and can be used to classify the black holes into different classes. When the charge is present, we find that the topological number is independent on the values of the parameters, and the charged Gauss-Bonnet AdS black holes can be divided into the same class of the RNAdS black holes with the same topological number 1. However, when the charge is absent, we find that the topological number has certain dimensional dependence. This is different from the previous studies, where the topological number is found to be a universal number independent of the black hole parameters. Furthermore, the asymptotic behaviors of curve {\tau}(r_h) in small and large radii limit can be a simple criterion to distinguish the different topological number. We find a new asymptotic behavior as {\tau}(r_h \to 0) = 0 and {\tau}(r_h \to \infty) = 0 in the black hole system, which shows topological equivalency with the asymptotic behaviors {\tau}(r_h \to 0)=\infty and {\tau}(r_h \to \infty)=\infty. We also give an intuitional proof of why there are only three topological classes in the black hole system under the condition (\partial_{r_h} S)P > 0.