论文标题
黑洞和de Sitter空间的梯子对称性：爱情数字和准模式
Ladder Symmetries of Black Holes and de Sitter Space: Love Numbers and Quasinormal Modes
论文作者
论文摘要
在本说明中，我们提出了（4D）黑洞和DE安慰空间（Spin 0）扰动的几何对称性概要。对于黑洞，我们专注于静态扰动，为此，（确切的）几何对称性具有SO的组结构（1,3）。发电机由三个空间旋转组成，并遵守特殊的旋律条件的三个保形杀伤向量。静态扰动解决方案构成了该组的单一（主要系列）表示。最近发现的梯子对称性源于这种表示结构。他们解释了黑洞爱情数字的众所周知的消失。对于De Sitter空间周围的动态扰动，从SO（1,4）等轴测图中，几何对称性并不令人惊讶。众所周知，准溶液构成等轴测组的非单身表示。我们为与此表示相关的梯子操作员提供明确的表达式。在这两种情况下，梯子结构都有助于将地平线的边界条件与无穷大（黑洞）或原点（De Sitter空间）连接起来，并且它们表现为超几何解决方案的连续关系。
In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For black holes, we focus on static perturbations, for which the (exact) geometric symmetries have the group structure of SO(1,3). The generators consist of three spatial rotations, and three conformal Killing vectors obeying a special melodic condition. The static perturbation solutions form a unitary (principal series) representation of the group. The recently uncovered ladder symmetries follow from this representation structure; they explain the well-known vanishing of the black hole Love numbers. For dynamical perturbations around de Sitter space, the geometric symmetries are less surprising, following from the SO(1,4) isometry. As is well known, the quasinormal solutions form a non-unitary representation of the isometry group. We provide explicit expressions for the ladder operators associated with this representation. In both cases, the ladder structures help connect the boundary condition at the horizon with that at infinity (black hole) or origin (de Sitter space), and they manifest as contiguous relations of the hypergeometric solutions.
