黑洞量子化及线性扰动理论的研究

This project mainly focuses on the quantization and linear perturbation theory of black holes. Firstly, we will study the quantization of the horizon area and entropy of black holes in several modified gravity theories. The methods used here include the calculation based on the action variable and periodicity. The characteristics of the quantum spectrum and the relic of the black hole will be discussed. Also, the generalization of the quantum tunneling method to the dynamic black hole is studied. Secondly, we will research the quasinormal modes of the dynamical black hole in general relativity and black holes in several modified gravity theories. Based on this kind of work, the linear stability of black holes will be discovered which is helpful in studying the quantization more completely. Finally, because of the discovery of the AdS/CFT duality, we will apply the linear perturbation theory of the black hole to the study of the effects on holographic superconductor and holographic thermalization in the modified gravity frame. This will help us in searching the nonequilibrium properties of the conformal field. The subject in our project is one of the hot topics in the research of theoretical physics and astrophysics. The achievement of this project will accelerate the development of the fundamental science including physics and astronomy. In particular, the comprehensive research of the quantization of the black hole will help the physicists to understand the relationship between the quantum effect of gravity and classical perturbation. This will improve the development of the study of quantum gravity. On the other hand, the linear perturbation theory of the black hole will not only help us to understand the application of the AdS/CFT duality in condensed matter field, but also give us a more complete description of the black hole physics. Additionally, the results will provide the direction and information to the astronomical observation in the future.

本项目主要关注黑洞的量子化及线性扰动理论。首先，我们将基于作用量变量和周期性对部分修正引力理论中的黑洞视界面积和熵进行量子化，分析量子谱的特征和黑洞遗迹现象，同时推广隧穿机制讨论动态黑洞的量子特征。然后，我们将细致研究动态黑洞、部分修正引力理论中的黑洞的拟正则模，讨论线性稳定性，进一步研究黑洞的量子化。最后，我们将基于AdS/CFT对应，应用黑洞线性扰动理论研究修正引力理论对全息超导和全息热化的影响，探讨共形场的非平衡物理性质。 本项目研究的问题是目前理论物理和天文学研究的热点问题之一，项目的成果将会推动基础物理和天文学的发展。其中对黑洞量子化的深入研究有助于弄清楚引力量子效应和经典扰动之间的关系，推动量子引力理论的发展。另一方面，黑洞线性扰动理论的研究不仅有助于深入理解AdS/CFT对应在凝聚态物理中的应用，而且还能深入认识黑洞的物理特征，为未来天文学观测提供重要依据。

黑洞物理问题是当前理论物理和天文物理研究中的热点问题之一。本项目关注黑洞的物理性质，主要围绕黑洞量子化和线性扰动理论中的问题开展研究。首先，我们发展了隧穿机制思想，推广弯曲时空量子场论方法去研究黑洞的量子效应。研究结果发现：黑洞的熵谱比面积谱更能体现黑洞的量子特征；近视界的共形对称性在Unruh真空发现热辐射起到了重要的作用；高维黑洞的霍金辐射谱与粒子的性质结构无关，而与高维背景的额外维尺度相关。然后，我们研究修正引力理论，构建新的全息热化模型，讨论修正参数对QCD热化过程的影响。研究的结果提供了一些具有更宽范围的热化时间的热化模型。此外，我们对带荷AdS黑洞的热力学性质进行了研究，发现在全息纠缠熵-温度相平面，该类黑洞具有类似于范德瓦尔斯流体类似的相结构。最后，在粘性色流体力学理论框架下我们对QGP的物理性质进行了研究，发现粘滞性对夸克的涨落能量获得有显著影响，碰撞显著地改变了折射率的行为。因此，我们的研究为量子引力的理论研究提供了新的线索，并且对探测额外维以及QGP的实验研究具有积极的指导意义。