Near horizon black holes in diverse dimensions and integrable models

TL;DR

This paper explores the near horizon geometries of extremal rotating black holes in various dimensions, deriving new integrable models with specific symmetries, and identifying connections to known systems like the Higgs oscillator.

Contribution

It introduces a novel integrable Hamiltonian framework for near horizon black hole geometries with SO(2,1) x U(n) symmetry, extending understanding of their symmetry structures.

Findings

Derived a new integrable Hamiltonian with U(n) symmetry

Connected the models to Higgs oscillator and Pöschl-Teller systems

Analyzed reductions by discarding cyclic variables

Abstract

The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally symmetric configuration and derive from it a new integrable Hamiltonian mechanics with U(n) symmetry. A further reduction of the model is discussed, which is obtained by discarding cyclic variables. A variant of the Higgs oscillator and the Poschl-Teller system show up in four and five dimensions, respectively.