Conformal mechanics inspired by extremal black holes in d=4

TL;DR

This paper constructs a canonical transformation linking the dynamics of a relativistic particle near an extremal black hole horizon in four dimensions to conformal mechanics, using action-angle variables and Liouville integrability.

Contribution

It introduces two methods for relating black hole near-horizon dynamics to conformal mechanics through canonical transformations.

Findings

Established a transformation using action-angle variables.

Derived a transformation based on Liouville integrability.

Enhanced understanding of black hole near-horizon symmetries.

Abstract

A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville.