Abstract
A toy model of gravitational collapse in General Relativity is studied. It consists of a spherically symmetric thin shell of dust with a fixed rest mass. The configuration space is the half-axis and the Hamiltonian splits into a differential operator of infinite order (“free” Hamiltonian) and a “Coulomb” potential. Harmonic analysis on the half-axis is used to define the free Hamiltonian. For rest masses comparable to, or lower than one Planck mass, the Kato-Rellich theorem is applicable and one self-adjoint extension of the full Hamiltonian is found. A boundary condition for the wave function results whose effect is to keep the shell away from the singularity. This will lead to superposition of states containing both black and white holes.
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Communicated by N. Yu. Reshetikhin
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Hajicek, P. Quantum mechanics of gravitational collapse. Commun.Math. Phys. 150, 545–559 (1992). https://doi.org/10.1007/BF02096961
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DOI: https://doi.org/10.1007/BF02096961