标题： 三维E$_{6}$引力的黑洞解 显示英文标题

标题： Black hole solutions of three dimensional E$_{6}$-gravity

摘要： 本文旨在构造带有所谓的 E$_{6}$电荷的例外Banados-Teitelboim-Zanelli（BTZ）黑洞，作为具有 E$_{6}$边界条件的三维高自旋Anti-de Sitter（AdS）引力的解。在实形式的 e$_{6} $李代数的Tits-Satake图的指导下，我们构建了三个显著的 E$_{6}$-高自旋黑洞模型：线性例外和正交例外BTZ解源于在 E$_{6\left( 6\right)}$的Tits-Satake图中分裂极值节点，而纯例外-例外模型则来自折叠到F$_{4\left( 4\right) }$。借助Hasse图可视化，我们研究了由此产生的高自旋谱，并使用两种规范变换来发展相应的度规。 为完整起见，我们通过利用真空特征标因子与 E$_{6}$根系的根之间的一一对应关系来计算配分函数，从而研究标准 BTZ 黑洞与 E$_{6}$高自旋引力场耦合的热力学性质。 显示英文摘要

摘要： This paper aims to construct exceptional Banados-Teitelboim-Zanelli (BTZ) black holes carrying E$_{6}$ charges as solutions to the 3D higher spin Anti-de Sitter (AdS) gravity with E$_{6}$ boundary conditions. Guided by Tits-Satake graphs of real forms of the e$_{6} $ Lie algebra, we build three remarkable E$_{6}$-higher spin black hole models: the linear-exceptional and the ortho-exceptional BTZ solutions result from splitting the extremal nodes in the E$_{6\left( 6\right)}$ Tits-Satake diagram while the pure exceptional-exceptional model follows from the folding down to F$_{4\left( 4\right) }$. And with the help of Hasse diagram visualizations, we study the ensuing higher spin spectrums to develop the corresponding metrics using two types of gauge transformations. For completeness, we examine the thermodynamics of the standard BTZ coupled to E$_{6}$ higher spin gravity fields by computing the partition function exploiting a one to one correspondence between the factors of the vacuum characters and the roots of the E$_{6}$ root system.