扩展相空间黑洞相变的微观、统计诠释以及全息热机的研究

考虑宇宙学常数的变化，并将宇宙学常数对应为黑洞的热力学压强，扩展相空间黑洞热力学尤其是黑洞相变近几年已经成为国际研究前沿。深入挖掘扩展相空间黑洞相变理论机制，尤其从微观和统计的层面揭示其规律，具有重要的科学意义同时也具有很大的挑战性。本项目是申请人过去几年工作在理论上的深入以及应用上的拓展。研究内容包括：（1）探索暗能量和修正引力理论对全息热机效率的影响及影响机制；（2）利用热力学几何工具从微观上诠释扩展相空间有些AdS黑洞为何不存在类范德瓦耳斯气体的P-V临界现象；（3）结合Dvali和Gomoz提出的黑洞可以理解为引力子的玻色—爱因斯坦凝聚的视角，尝试从统计层面揭示扩展相空间黑洞相变的机理。后者是一项全新的课题，因而也是本项目最具挑战性的内容。本项目的研究一方面促进人们对全息热机以及在微观和统计层面对扩展相空间黑洞相变更深刻的理解，另一方面也将促进对暗能量和修正引力理论的理解。

Considering the variation of the cosmological constant and identifying the cosmological constant as thermodynamic pressure of black holes, the extended phase space thermodynamics especially black hole phase transition has become the international research frontier. Exploring the theoretical mechanism of black hole phase transition in the extended phase space, especially from the microscopic and statistical mechanical perspective, is both of great scientific importance and very challenging. This project is both the further probe in theory and extension in application of our work in the past few years. It consists of the following aspects. (1) Probe the influence of dark energy and modified gravity theories on the efficiency of holographic heat engine and the mechanism; (2)Utilize the thermodynamic geometry to explain from the microscopic perspective why some AdS black holes do not exhibit Van der Waals like P-V criticality; (3) From the perspective proposed by Dvali and Gomoz that black hole can be viewed as Bose-Einstein condensation of gravitons, disclose the mechanism of black hole phase transition in the extended phase space in the statistical level. The latter is a totally new approach, thus is the most challenging aspect in this project. This project will deepen the understanding of holographic heat engine and black hole phase transition in the microscopic and statistical level. On the other hand, it will also help understand dark energy and modify gravity theories.