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

Mathematics – Logic

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Einstein-Maxwell Spacetimes, Spacetimes With Fluids, Radiation Or Classical Fields

Scientific paper

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 GL(2,c) type and parasupersymmetry of arbitrary order or shape invariance, which originated from an SO(4,c) group.

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