Schrodinger Picture of Quantum 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.

9 pages, 1 figure. Matches published version

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• Gravitational collapse and Hawking-like radiation of the shell in AdS spacetime
• Quantum Collapse of a Thin Shell Revisited
• Semiclassical S-matrix for black holes
• Proper time Quantization of a Thin Shell
• A quantum thin shell surrounding a Black Hole