Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry

TL;DR

This paper develops an algebraic method to construct quasi-normal modes of extremal black holes, revealing that hidden conformal symmetry is an intrinsic property and crucial for understanding their perturbations.

Contribution

It introduces a novel algebraic approach to derive quasi-normal modes and clarifies the role of hidden conformal symmetry in extremal black holes.

Findings

Quasi-normal modes form infinite towers as descendents of highest weight modes.

Hidden conformal symmetry is intrinsic to extremal black holes.

Correct identification of hidden conformal symmetry is essential for physical modes.

Abstract

In this paper, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the descendents of the highest weight modes. Our investigation shows that the hidden conformal symmetry suggested in arXiv:1007.4269 is an intrinsic property of the extremal black hole. Moreover, we notice that we need to fix the freedom in defining the local vector fields and find the right hidden conformal symmetry to obtain the physical quasi-normal modes.