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Wave functions for quantum black hole formation in scalar field collapse

Dongsu Bak1,*, Sang Pyo Kim2,†, Sung Ku Kim3,‡, Kwang-Sup Soh4,§, and Jae Hyung Yee5,∥

  • 1Department of Physics, University of Seoul, Seoul 130-743, Korea
  • 2Department of Physics, Kunsan National University, Kunsan 573-701, Korea
  • 3Department of Physics, Ewha Women’s University, Seoul 120-750, Korea
  • 4Department of Physics Education, Seoul National University, Seoul 151-742, Korea
  • 5Department of Physics, Yonsei University, Seoul 120-749, Korea

  • *Electronic address: dsbak@mach.uos.ac.kr
  • †Electronic address: sangkim@knusun1.kunsan.ac.kr
  • ‡Electronic address: skkim@theory.ewha.ac.kr
  • §Electronic address: kssoh@phya.snu.ac.kr
  • ∥Electronic address: jhyee@phya.yonsei.ac.kr
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Phys. Rev. D 61, 044005 – Published 24 January, 2000

DOI: https://doi.org/10.1103/PhysRevD.61.044005

Abstract

We study quantum mechanically self-similar black hole formation by a collapsing scalar field and find the wave functions that give the correct semiclassical limit. In contrast with classical theory, the wave functions for 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 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=ħImlnψ. 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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Outline

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Phys. Rev. D 61, 044005– Published 24 January, 2000
  • Received 8 July 1999

© 2000 American Physical Society

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