Euclidean quantum gravity in a Kerr black hole ergosphere

Starting from the dynamics of a scalar field on a Kerr metric, we propose an analytical extension of spacetime coordinates (with Boyer–Lindquist coordinates) for a closed system with no flow at the boundary, and we apply the polynomial conditions for confluent Heun functions with the aim to find the distribution of the energy levels for the scalar field that describes the spacetime inside the ergosphere of a Kerr black hole. We obtain discretizations of the mass and angular momentum that can be motivated from the expression of each energy level.