Symmetries of the near horizon of a Black Hole by Group Theoretic methods

TL;DR

This paper employs group theoretic methods to identify and analyze the symmetries of quantum and classical dynamics near a black hole horizon, revealing underlying Lie algebra structures.

Contribution

It introduces a systematic group theoretic approach to uncover symmetries in black hole near horizon physics and related classical systems.

Findings

Extended Lie point symmetries for quantum black hole probing

Lie algebra generators for classical charged particle dynamics

Symmetry structures in inverse square potential and monopole fields

Abstract

We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged particle in the field of an inverse square potential and a monopole, in the presence of certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries.