Solutions of (2+1)-dimensional Einstein-Maxwell theory with parasupersymmetry

Abstract

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