任意时空维度上黑洞近视界性质和黑洞熵起源问题研究

The study of common features of black holes in generic dimensions could offer invaluable insights to the understanding of the quantum origin of black hole entropy. In the process, properties of gravity near the black hole horizon play a key role. Guage/Gravity duality has led people to believe that the quantum property of a black hole is likely governed by a conformal field theory; we have found in [CQG29(2012)] a new way to reveal the conformal symmetry enjoyed by the gravitational action near a black hole horizon, and this has enabled us to discover that in higher dimensions, the gravitaional interaction near a black hole horizon has a much larger symmetry than the conformal group[PRD(2014)accepted]. In this project we want to develop upon the new findings and to study the near horizon properties of a black hole in generic spacetime dimensions systematically. We expect this to provide further evidence for the general Black Hole/Conformal (or other higher symmetry) Field Theory correspondence. We want to achieve two key goals in this project. Firstly, we want to use our new method to find and classify all intrinsic symmetries of the gravitational interaction near a black hole horizon in generic dimensions. Secondly, although our new method has helped us find new symmetries in higher dimensions, it has also broghout new technical challenges. Especially, traditional ways of calculating the black hole entropy can no longer be used directly. We need to develop new techniques to overcome this difficulty and to obtain prediction on the black hole entropy by the newly found symmetries.

对任意时空维度上黑洞之间共同特性的研究可以为进一步理解黑洞熵起源问题提供宝贵线索。这个过程中引力在黑洞视界附近的性质起着关键作用。规范/引力对偶暗示黑洞的量子特性很可能由一个共形场论来描述；我们在[CQG29(2012)]中提出新思路来揭示引力作用量如何在黑洞视界附近获得共形对称性，由此还进一步发现在高时空维度上引力在黑洞视界附近具有的比共形对称性大得多的对称群[PRD(2014)已接受]。本项目将以此为基础对任意时空维度上黑洞的近视界性质作系统研究，这有望为任意维度上的黑洞/共形（或其它高对称性）场论对偶提供更详细的证据。我们将力图实现两个关键目标：1）找到引力在任意维度黑洞视界附近所具有的完整内禀对称性，并对之进行分类；2）我们的新方法在帮助找到新对称性的同时也在预言黑洞性质方面带来巨大挑战，使之前用来计算黑洞熵的方法都不再直接适用；我们需要发展新的技术来获得新对称性对黑洞熵的预言。

量子引力理论是现代理论物理研究的最重要目标之一，为黑洞熵找到一个正确的理论解释有望为发现量子引力理论提供一个突破口。人们于1997年发现了黑洞熵与黑洞所处时空背景上的渐进对称性之间的定量关系，又于2009年开始针对极端黑洞建立了黑洞熵与黑洞视界上渐进对称性之间的定量关系。将后者推广到任意时空维度的任意黑洞是本项目的主要目标。通过本项目研究，我们发现通过定义适当的边界条件，任意时空维度的黑洞视界附近都存在扩展BMS对称性，其中由超转动算符构成的子代数与我们在2014年发现的类-Witt代数一致。所发现的扩展BMS代数的荷与黑洞的熵和角动量存在密切联系，这项工作发表在PRD95(2017)104053。此外，还可以利用探针物质场来研究背景时空的渐进对称性。我们首次证明，麦克斯韦方程在Kerr黑洞和Kerr-Newman-NUT-AdS黑洞的近视界区域都具有隐藏共形对称性。这项工作发表在 JHEP 1804 (2018) 001。上述论文均被SCI收录，相关研究成果对于深入认识黑洞近视界对称性存在的普遍性，进一步挖掘黑洞近视界对称性与黑洞熵之间的联系等都有重要的研究价值。