Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, People's Republic of China.
Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Phys Rev Lett. 2019 Aug 16;123(7):071103. doi: 10.1103/PhysRevLett.123.071103.
The Ruppeiner geometry of thermodynamic fluctuations provides a powerful diagnostic of black hole microstructures. We investigate this for charged anti-de Sitter black holes and find that, while an attractive microstructure interaction dominates for most parameter ranges, a weak repulsive interaction dominates for small black holes of high temperature. This unique property distinguishes the black hole system from that of a van der Waals fluid, where only attractive microstructure interactions are found. We also find two other novel universal properties for charged black holes. One is that the repulsive interaction is independent of the black hole charge and temperature. The other is that the behavior of the Ruppeiner curvature scalar near criticality is characterized by a dimensionless constant that is identical to that for a van der Waals fluid, providing us with new insight into black hole microstructures.
鲁佩尔纳热力学涨落几何为黑洞微结构提供了一种强大的诊断工具。我们研究了带电反德西特黑洞的情况，发现尽管在大多数参数范围内，吸引力主导着微结构相互作用，但在高温小黑洞中，弱斥力主导着微结构相互作用。这种独特的性质将黑洞系统与范德瓦尔斯流体区分开来，在范德瓦尔斯流体中，只发现了吸引力的微结构相互作用。我们还发现了带电黑洞的另外两个新颖的普遍性质。一个是斥力相互作用与黑洞电荷和温度无关。另一个是，在临界点附近，鲁佩尔纳曲率标量的行为特征是一个无量纲常数，与范德瓦尔斯流体的常数相同，这为我们深入了解黑洞微结构提供了新的视角。
