Wave functions for quantum black hole formation in scalar field collapse -art. no. 044005

We study quantum mechanically self-similar black hole formation by a collap sing scalar field and find the wave functions that give the correct semicla ssical limit. In contrast with classical theory, the wave functions for bla ck hole formation even in the supercritical case have not only incoming flu x but also outgoing flux. From this result we compute the rate for black ho le formation. In the subcritical case our result agrees with the semiclassi cal tunneling rate. Furthermore, Re show how to recover the classical evolu tion of black hole formation from the wave function by defining the Hamilto n-Jacobi characteristic function as W=(h) over bar Im ln psi. We find that the quantum-corrected apparent horizon deviates from the classical value on ly slightly without any qualitative change even in the critical case.