Quasinormal frequencies using the hidden conformal symmetry of the Schwarzschild black hole

TL;DR

This paper investigates the hidden conformal symmetry of Schwarzschild black holes and finds it originates from the AdS$_2$ sector, revealing limitations in using this symmetry to describe certain quasinormal modes.

Contribution

It clarifies the geometric origin of the hidden conformal symmetry and its implications for quasinormal mode analysis in Schwarzschild black holes.

Findings

Hidden conformal symmetry arises from AdS$_2$ sector, not Rindler space.

Purely imaginary quasinormal frequencies are not suitable for describing damped modes.

Limitations of conformal symmetry approach in black hole perturbation analysis.

Abstract

We show that the hidden conformal symmetry of the Schwarzschild black hole is realized from the AdS$_2$ sector of the AdS$_2\times S^2$, but not from the Rindler spacetime which is the genuine near-horizon geometry of the Schwarzschild black hole. This implies that purely imaginary quasinormal frequencies obtained using the hidden conformal symmetry is not suitable for describing the largely damped modes around the Schwarzschild black hole.