Horizon Quantum Mechanics: spherically symmetric and rotating sources

In this paper we discuss some mathematical aspects of the horizon wave-function formalism, also known in the literature as horizon quantum mechanics. In particular, first we review the structure of both the global and local formalism for static spherically symmetric sources. Then, we present an extension of the global analysis for rotating black holes and we also point out some technical diffculties that arise while attempting the local analysis for non-spherically symmetric sources