Wave Functions for Quantum Black Hole Formation in Scalar Field Collapse

Details Wave Functions for Quantum Black Hole Formation in Scalar Field Collapse Wave Functions for Quantum Black Hole Formation in Scalar Field Collapse

1999-07-08

arxiv.org/abs/gr-qc/9907032v3

Phys.Rev. D61 (2000) 044005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTex, 14 pages, no figures; Eq. (36) and references added; revised version for PRD

Scientific paper

10.1103/PhysRevD.61.044005

We study quantum mechanically the self-similar black hole formation by collapsing scalar field and find the wave functions that give the correct semiclassical limit. In contrast to classical theory, the wave functions for the black hole formation even in the supercritical case have not only incoming flux but also outgoing flux. From this result we compute the rate for the black hole formation. In the subcritical case our result agrees with the semiclassical tunneling rate. Furthermore, we show how to recover the classical evolution of black hole formation from the wave function by defining the Hamilton-Jacobi characteristic function as $W = \hbar {\rm Im} \ln \psi$. We find that the quantum corrected apparent horizon deviates from the classical value only slightly without any qualitative change even in the critical case.

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