pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes

TL;DR

This paper explores the emergent symmetries in black hole quasinormal modes using Penrose limits, revealing geometric structures that explain spectral features and distinguish QNM solutions from scattering states.

Contribution

It generalizes the Penrose limit approach to analyze symmetries of QNMs for Schwarzschild black holes and horizon generators, linking geometric limits to spectral properties.

Findings

Near-ring scaling limit reveals emergent symmetries of QNM spectrum.

Penrose limit on horizon generators uncovers near-horizon symmetries.

Symmetry considerations distinguish QNM solutions from scattering states.

Abstract

There are two interesting classes of trapped null geodesics in any black hole spacetime: those that lie on the photon ring and those that generate the horizon. Recent work introduced a "near-ring" scaling limit that exhibits the emergent symmetries of the eikonal quasinormal mode (QNM) spectrum associated to the photon ring. This analysis was reformulated geometrically by Fransen using the Penrose limit, which produces pp-waves from geodesics. We elaborate on and generalize various aspects of this construction for the Schwarzschild black hole. We also discuss the Penrose limit onto the horizon generators. This second limit, although technically simpler, also displays emergent near-horizon symmetries that explain the equally-spaced overtones of the highly-damped QNM spectrum. In both examples, symmetry considerations distinguish the QNM solutions from the scattering states and produce overtones as descendants.