Chong-Sun Chu

It was proposed in \cite{Chu:2024qil} that a quantum black hole can be described by a fuzzy sphere together with a half-filled Fermi sea. In this paper we propose that the tunneling of a fuzzy sphere system to a small one describes the quantum decay of black hole by Hawking radiation. Since the Fermi sea shrinks and the quantum mechanical Hamiltonian conserves fermion number, the amplitude of transition naively vanishes unless the tunneling path provides exact number of zero modes to soak up the excess fermi states. We show that a monopole on fuzzy sphere does exactly that. This fixes the tunneling path. The resulting tunneling rate reproduces Page's result for the semi-classical decay rate of black hole. We propose to identify the fermi states released by the monopole as the Hawking radiation. At the level of probability, the Hawking radiation is found to be given by a Boltzmann distribution at the Hawking temperature. One can go beyond the probabilistic description by determining the full wave function of the multi-partite Hawking quanta. This is possible with a real time formulation of the tunneling process. Unitarity is manifest in our quantum mechanics.