2+1-Gravity and The Embedding its Dynamiycal Symmetry and Para-Supersymmetry into SO(4,c) Group

TL;DR

This paper explores special Einstein-Maxwell solutions with magnetic monopoles, analyzing their quantum mechanics and revealing underlying symmetries like SO(4,c) and para-supersymmetry, contributing to understanding of 2D Hamiltonian degeneracies.

Contribution

It introduces a novel connection between 2D Hamiltonian degeneracies, para-supersymmetry, and the SO(4,c) group within Einstein-Maxwell solutions.

Findings

Solutions exhibit static spacetime with constant curvature and magnetic monopoles.

Quantum mechanics in these spacetimes shows degeneracy groups of GL(2,c) type.

Hamiltonians possess para-supersymmetry and shape invariance originating from SO(4,c).

Abstract

Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its spatial part and a constant magnetic field of a magnetic monopole together with deficit of angle at the location of point mass. The quantum mechanics of a point particle in these spacetimes in the absence of angular deficit has been solved algebraically both relativistically and non-relativistically. It has been also shown that these 2-dimensional Hamiltonians have the degeneracy group of GL(2,c) type and para-supersymmetry of arbitrary order or shape invariance, which is originated from a SO(4,c) group.