Schrodinger Picture of Quantum Gravitational Collapse

TL;DR

This paper employs the functional Schrödinger equation to analyze quantum gravitational collapse, incorporating backreaction effects and defining a black hole operator, revealing an energy-black holeness uncertainty relation.

Contribution

It introduces a novel quantum approach to gravitational collapse using the Schrödinger picture, including backreaction and a new black hole operator.

Findings

Black hole operator eigenstates identified

Energy and black holeness do not commute, implying an uncertainty relation

Derived a PDE for time-dependent gravitational collapse

Abstract

The functional Schrodinger 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 Schrodinger 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.