A Self-consistent Model of Quantum Black Hole

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What is the black hole in quantum mechanics? We examine this problem in a self-consistent manner. First, we analyze time evolution of a 4D spherically symmetric collapsing matter including the back reaction of particle creation that occurs in the time-dependent spacetime. As a result, a compact high-density star with no horizon or singularity is formed and eventually evaporates. This is a quantum black hole. We can construct a self-consistent solution of the semi-classical Einstein equation showing this structure. In fact, we construct the metric, evaluate the expectation values of the energy momentum tensor, and prove the self-consistency under some assumptions. Large pressure appears in the angular direction to support this black hole, which is consistent with 4D Weyl anomaly. When the black hole is formed adiabatically in the heat bath, integrating the entropy density over the interior volume reproduces the area law.