Quantum gravitational collapse as a Dirac particle on the half-line

Abstract

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum $|E|<m$, and a continuum of scattering states for $|E|>m$, where $m$ is the rest mass of the shell and $E$ is the Arnowitt-Deser-Misner mass. For sufficiently large $m$, the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.

6 pages, 5 figures; Title change. Matches published version

References in corpus (3)

• Quantum Nature of the Big Bang
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Polymer Quantization of a Self-Gravitating Thin Shell