标题： 黑洞在修改引力中的隐藏共形对称性 显示英文标题

标题： Hidden conformal symmetries for black holes in modified gravity

摘要： 我们确定了在矢量-张量引力理论中黑洞扰动演化方程背后的隐藏共形对称性。 这些隐藏对称性在球对称、渐近平坦的黑洞几何外部区域处处有效。 它们使我们能够将控制黑洞扰动的二阶算子分解为两个可对易的一阶算子的乘积。 作为结果，我们能够解析地确定黑洞扰动方程的最一般时间依赖解。 我们关注属于共形对称性的最高权表示的解，表明它们对应于进入黑洞视界的准束缚态，并在空间无穷远处指数衰减。 它们的时间依赖性由纯虚数频率表征，虚部由整数间隔分开，如同广义相对论中的准正则模态的泛音。 显示英文摘要

摘要： We determine hidden conformal symmetries behind the evolution equations of black hole perturbations in a vector-tensor theory of gravity. Such hidden symmetries are valid everywhere in the exterior region of a spherically symmetric, asymptotically flat black hole geometry. They allow us to factorize second order operators controlling the black hole perturbations into a product of two commuting first order operators. As a consequence, we are able to analytically determine the most general time-dependent solutions for the black hole perturbation equations. We focus on solutions belonging to a highest weight representation of a conformal symmetry, showing that they correspond to quasi-bound states with an ingoing behaviour into the black hole horizon, and exponential decay at spatial infinity. Their time-dependence is characterized by purely imaginary frequencies, with imaginary parts separated by integer numbers, as the overtones of quasi-normal modes in General Relativity.