高维Kerr-Nut-Ads及相关黑洞性质的场论研究

The Ads/CFT is the main fundamental subject in General Relativity, and an issue frequently examined is how far one can go under this correspondence. Usually, one can check this conjecture through comparisons of the decay rates of various propagating waves on a variety of spacetime backgrounds with the results computed in corresponding CFT’s, or Quasi-normal modes of black hole spacetime matched to the poles of correlation functions of CFT. Based on the decay rate of excitations of a massive rotating star and quasi-normal mode methods, we will analyze the behavior of gravity wave in high-dimensional Kerr-Nut-Ads back ground and the related results of CFT on the boundary. Consequently, one can check the Kerr/CFT correspondence, and solve some the related field problems. The detail study contents include: (1) Consider the geometry symmetry of the near horizon extreme Kerr-Nut-Ads black holes and other black holes, we will discuss the constrains of the symmetry on the matter fields and find the solutions; (2) Based on the special solution of extreme Kerr-Nut-Ads black holes and similar black holes, by investigating the radiation of massive rotating star and computing the related field quantities, we check the Kerr/CFT correspondence; (3) Apply the related properties of near horizon of extreme Kerr-Nut-Ads and other black holes, we study the magnetosphere and its related stability. This project focuses on the physical properties of high-dimensional Kerr-Nut-Ads black holes and similar black holes at the near horizon and the field quantities, in order to shed light on a better understanding of spacetime structure, Kerr/CFT correspondence and gravitational waves.

Ads/CFT对应是引力理论中重要的主要基础问题之一，人们需要检验该假设成立的范围，通常可以通过计算各种时空背景下波的衰变率与共形场论的结果、或黑洞背景下准正模与共形场关联函数的极点进行比对。项目拟基于极端转动黑洞视界附近的转动星的激发衰变率与边界共形场论的分析、准正模计算等方法，分析高维Kerr-Nut-Ads等一类极端黑洞视界附近场论的行为，从而验证Kerr/CFT对应关系，解决与此有关的各种具体问题。具体研究内容包括：（1）考虑Kerr-Nut-Ads 等极端黑洞在视界附近的对称性对物质场的限制，给出相应的解形式；（2）基于Kerr-Nut-Ads 等在极端黑洞视界附近特定解，分析绕黑洞转动的星体运动的辐射，计算相关的物理量，验证Kerr/CFT对应（3）研究与之相关联的磁球的解以及稳定性问题，进而分析黑洞的性质等。

本项目详细研究了一类非爱因斯坦引力黑洞的热力学与PV相变，发现高维有质量引力的重入相变、类气液固的相变，即大黑洞/中黑洞、小黑洞的相变。运用准正模方法研究研究黑洞的稳定应，揭示相变与准正模变化的依赖关系。解析地给出quintessence背景下的新型Kerr黑洞解，并给出了相应物理参数的限制，其热力学量满足黑洞热力学定律，克服了已有模型的缺陷。在研究Kerr类黑洞的扰动解时，我们发现标量扰动的准正模在外源驱动下，除去保持不变的频谱外，还会导致新的频谱出现。通过解析和数值两种方法，采取多种的截断和近似有效势，证明：只要采取不连续的有效势，都会带来准正谱的急剧变化，从而有别于解析结果，并且运用WKB方法证明其普适性，解释文献中相互矛盾结论的原因。这一结果可能会对从测量的引力波如何提取必要信息的方法产生影响。