Kerr/CFT对偶及其相关问题的研究

Holographic dual between general stationary rotating black holes and conformal field theory (Kerr/CFT dual) is a basic frontier problem in current research field of relativistic gravitation theory. This project is devoted to develop and consummate the theory of Kerr/CFT dual, which will help us to gain insights into many aspects of quantum gravity, such as microcosmic origin of black hole entropy, Hawking radiation of black hole and holographic properties of gravity. The research contents of this project are briefly listed as following. (1) To consider closely the hidden conformal symmetry of scalar field, to find its new realization way, and to study how to uncover the hidden conformal symmetry of spin-nonzero perturbation fields. (2) To research the geometric origin of hidden conformal symmetry, and to explore how to calculate the central charge in non-extremal Kerr/CFT dual. (3) To explore a new mechanism of Hawking radiation by combining Kerr/CFT dual and Hawking radiation. This consideration can be motivated by the quantum anomaly model to derive Hawking radiation. (4) To study how to calculate logarithmic corrections and higher derivative gravity corrections to Bekenstein-Hawking area entropy in the framework of Kerr/CFT dual.

一般稳态转动黑洞与共形场理论的全息对偶（Kerr/CFT对偶）是当前相对论引力理论研究领域的基础前沿课题。本项目将致力于发展和完善Kerr/CFT对偶的理论，以获取我们对于黑洞熵的微观起源、Hawking辐射以及引力全息性质等方面的一些新的认识和理解。本项目的主要研究内容包括：（1）对标量场所反映出的隐藏共形对称性质进行再研究，寻找其新的实现方式，并且对非零自旋微扰场的隐藏共形对称性进行研究；（2）深入研究隐藏共形对称性的几何根源，探索如何计算非极端Kerr/CFT对偶的中心荷问题；（3）提出将Kerr/CFT对偶性与Hawking辐射结合起来研究，借鉴量子反常模型，探索Hawking辐射新的物理机制；（4）在Kerr/CFT对偶性的框架内研究Bekenstein-Hawking面积熵的对数项修正和高阶导数引力理论的修正。

在本项目的支持下，我们主要完成了一下研究工作：（1）研究了五维Kerr-Godel黑洞中标量场的的超辐射不稳定性；（2）证明了GHS黑洞在带电标量场扰动下是稳定的；（3）解析和数值地计算了施加狄利克雷边界条件下带电标量场在GHS黑洞背景中的超辐射不稳定性，给出了不稳定模式的解析表达式和数值计算结果，发现了快速增长模式的存在；（4）研究了GHS黑洞与标量场复合系统超辐射不稳定性的线性时间演化问题；（5）研究了以运动星体为引力源所发射的标量波和引力波的微观共形场解释的问题。（6）我们还研究了一些黑洞的Hawking辐射问题。