Hidden Supersymmetry in Dirac Fermion Quasinormal Modes of Black Holes

TL;DR

This paper reveals that Dirac fermion quasinormal modes in black hole backgrounds are linked to an N=2 supersymmetric quantum mechanics algebra, showing unbroken supersymmetry for both massless and massive cases.

Contribution

It demonstrates a novel connection between black hole fermionic quasinormal modes and supersymmetric quantum mechanics, extending to massive fermions.

Findings

Unbroken supersymmetry in massless fermion quasinormal modes.

Supersymmetry remains unbroken for massive fermions.

Establishes a bijective correspondence between quasinormal modes and zero modes.

Abstract

We connect the quasinormal modes corresponding to Dirac fermions in various black holes backgrounds to an N=2 supersymmetric quantum mechanics algebra, which can be constructed from the radial part of the fermionic solutions of the Dirac equation. In the massless fermion case, the quasinormal modes are in bijective correspondence with the zero modes of the fermionic system and this results to unbroken supersymmetry. The massive case is more evolved but as we prove, supersymmetry remains unbroken even in this case.