Topology of zero riemann curvature flat space in supergravity

The equation of motion of the gravitino is investigated in a flat space reduced from the Kerr geometry by taking the massless limit of the gravitational source. We adopt the ansatz ψ_μ(x)=δ_μoψ(x), i.e., the Coulomb potential analogue to the Rarita-Schwinger Majorana field of the gravitino. A non-trivial exact classical solution of ψ(x) is obtained and it is interpreted as the source of the intrinsic topology of the background flat space. This flat space is spanned by two Minkowski sheets interconnected through a disk of radius a (the angular momentum parameter in the Kerr geometry).