论文标题
高斯河畔黑洞在广告空间中的拓扑确定性
The topological natures of the Gauss-Bonnet black hole in AdS space
论文作者
论文摘要
在最近的提案中[物理学。莱特牧师。 129，191101（2022）]，使用通用的脱壳自由能将黑洞视为拓扑热力学缺陷。在本文中，我们遵循这样的提议，研究广告空间中高斯黑洞的局部和全球拓扑表现。局部拓扑表现由绕组数反射，其中正绕组和负绕组数对应于稳定且不稳定的黑洞分支。全球拓扑表现由拓扑数反映出，这些数字被定义为所有黑洞分支的绕组数量之和，可用于将黑洞分类为不同的类别。当电荷存在时，我们发现拓扑数在参数的值上是独立的，并且带电的高斯 - 邦网广告黑洞可以分为相同的rnads黑孔，具有相同的拓扑编号1。但是，当电荷不存在时，我们发现拓扑数具有一定的尺寸依赖性。这与以前的研究不同，在先前的研究中，拓扑数是一个通用数字，与黑洞参数无关。此外，在大小半径限制中，曲线τ（R_H）的渐近行为可能是区分不同拓扑数的简单标准。我们在黑洞系统中发现了一种新的渐近行为为τ（r_h \ to 0）= 0 = 0和τ（r_h \ to \ infty）= 0，它显示了与渐近行为τ（r_h \ t \ t r_h \ t t the）拓扑等效性（r_h \ t of the）= \ infty和τ（r_h \ ftty andτ（r_h \ f \ f \ f \ f \ infty）= \ suffty。我们还提供了一个直觉证明，说明为什么黑洞系统中只有三个拓扑类别（\ partial_ {r_h} s）p> 0。
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 τ(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 τ(r_h \to 0) = 0 and τ(r_h \to \infty) = 0 in the black hole system, which shows topological equivalency with the asymptotic behaviors τ(r_h \to 0)=\infty and τ(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.
