Darboux Covariance: A Hidden Symmetry of Perturbed Schwarzschild Black Holes

TL;DR

This paper uncovers a hidden symmetry called Darboux covariance in the perturbations of Schwarzschild black holes, linking various master equations and preserving key physical quantities like quasinormal modes.

Contribution

It demonstrates that all master equations for Schwarzschild perturbations are connected through Darboux transformations, revealing a new symmetry in black hole perturbation theory.

Findings

Darboux transformations connect different master equations.

Physical quantities like quasinormal modes are preserved.

A hierarchy of conserved quantities remains invariant.

Abstract

Starting from the infinite set of possible master equations for the perturbations of Schwarzschild black holes, with master functions linear in the metric perturbations and their first-order derivatives, we show that of all them are connected via Darboux transformations. These transformations preserve physical quantities like the quasinormal mode frequencies and the infinite hierarchy of Korteweg-de Vries conserved quantities, revealing a new hidden symmetry in the description of the perturbations of Schwarzschild black holes: Darboux covariance.