Quantum collapse of a self-gravitating thin shell and statistical model of quantum black hole

The quantum collapse of a self-gravitating thin shell in the minisuperspace models is revisited on the assumption that the shell is composed of N distinguishable identical particles. The ground state of the shell is found and defined as a quantum black hole (QBH). We show that the energy of single particle in the QBH is dependent on N, and N has an up-limit for a stable QBH. The effective exciting energy of single particle is determined, which is universally 1/2 of the Planck energy for the full-filled QBHs. We also propose a simple statistical model of QBH and show that a QBH is full-filled at low temperatures and half-filled at high temperatures. The specific heat of QBH is found to be positive at low temperatures and the relation of the QBH mass with its temperature is obtained in the high-temperature limit of our model.