**Schematic diagram of topology winding number Courtesy of the research group**

Recently, Wei Shaowen and Liu Yuxiao, professors of the gravitational team of the School of Physical Science and Technology of Lanzhou University, collaborated with Robert B. Mann, professor of the University of Waterloo, Canada, to study the topological properties of black hole solutions in thermodynamic parameter space using Φ mapping topological flow theory. After considering the black hole solution itself as a special topological defect, a topological number independent of the internal parameters of the black hole was constructed, and a new method for studying the thermodynamic topological properties of black holes was proposed, and the relevant research work was published in Physical Review Letters and selected as the editor’s recommended article in the current issue.

Black holes are celestial objects with such curvature of space-time that light cannot escape. Black hole thermodynamics is a major component of modern black hole physics. Since famous physicists such as Hawking and Bekenstein established black hole thermodynamics in the seventies of the last century, the thermodynamic properties of black holes have been widely studied and paid attention to. Because it involves many disciplines such as quantum mechanics, statistical physics and general relativity, the study of black hole thermodynamics is helpful to understand the nature of black holes and gravity, and is an effective way to deeply understand the theory of quantum gravity.

Based on the research basis of black hole phase transition, the research team proposed the “black hole micromolecule” model, pointing out that the interaction between the microscopic degrees of freedom of black holes can be investigated by studying the phase transition of small black holes, and the microscopic properties can be revealed with the help of macroscopic quantities such as the black hole Hawking temperature, which provides a new way to understand the microstructure of black holes. Furthermore, combined with the theory of fluctuations in statistical physics, a set of general methods to reveal the potential micromolecular interactions of black holes is developed, and it is found that different from general fluid systems, there can be repulsive interactions between microscopic molecules of black holes, revealing the uniqueness of the thermodynamic properties of black holes.

At present, topology, a mathematical tool, has been applied to various research fields of physics. In black hole thermodynamics, different types of black holes have different thermodynamic macroscopic quantities. For the same type of black hole, there may be different black hole phases at a specific temperature, which may or may not be locally stable. Whether it is possible to distinguish them topologically and give general conclusions is an interesting and important question.

Starting from the generalized free energy, the research team constructed a vector field whose zero point represents the black hole solution itself. With the help of this property, a new topological number is proposed by using the theory of topological flow of segment Φ mapping. From a local perspective, locally stable black hole phases have a positive number of local topology, while locally unstable have a negative number of local topology. Furthermore , for the same type of black hole , the sum of all local topological numbers yields the overall topological number. Then, from an overall perspective, black holes can be topologically classified according to the number of overall topologies. According to this classification, black holes with the same overall topological number (even if they are different types of black holes) have similar thermodynamic properties.

Since these topological numbers are universal constants that do not depend on the specific parameters of black holes, they are of great significance for understanding the nature of black holes and gravity, and may provide new clues to the establishment of quantum gravity theory. (Source: China Science News, Wen Caifei, Faisa)

Related Paper Information:https://doi.org/10.1103/PhysRevLett.129.191101