## Abstract

The functional Schrödinger equation is used to study the quantum collapse of a gravitating, spherical domain wall and a massless scalar field coupled to the metric. The approach includes backreaction of pre-Hawking radiation on the gravitational collapse. Truncating the degrees of freedom to a minisuperspace leads to an integro-differential Schrödinger equation. We define a 'black hole' operator and find its eigenstates. The black hole operator does not commute with the Hamiltonian, leading to an energy-black holeness uncertainty relation. We discuss energy eigenstates and also obtain a partial differential equation for the time-dependent gravitational collapse problem.

Original language | English (US) |
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Article number | 215007 |

Journal | Classical and Quantum Gravity |

Volume | 26 |

Issue number | 21 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)