Quantum particle probe of the Kerr naked singularity

Abstract

We investigate Kerr's timelike naked singularity within the framework of quantum mechanics. A quantum particle in the form of a massive boson is sent in the plane theta = pi/2 to the naked ring singularity of Kerr which develops for the overspinning case (a > M) to test it from a quantum picture. This singularity is analysed in two different coordinate systems. We show that the spatial operator of the Klein-Gordon equation both in Boyer-Lindquist and in the dragging coordinate systems has a unique self-adjoint extension. As a result, the classical Kerr's ring singularity becomes quantum regular, if it is probed with massive bosonic particles obeying the Klein-Gordon equation.