Quantum collapse of dust shells in 2+1 gravity

Abstract

This paper considers the quantum collapse of infinitesimally thin dust shells in 2+1 gravity. In 2+1 gravity a shell is no longer a sphere but a ring of matter. The classical equation of motion has been considered by Peleg and Steif and Cristosomo and Olea. The minisuperspace quantum problem can be reduced to that of a harmonic oscillator in terms of the curvature radius of the shell, allowing the use of well-known methods to find the motion of coherent wave packets that give the quantum collapse of the shell. Classically, as the radius of the shell falls below a certain point, a horizon forms. In the quantum problem one can define various quantities that give "indications" of horizon formation. Without proper definitions of a "horizon" in quantum gravity, these can be nothing but indications.

26 pages, 8 figures, in press, General Relativity and Gravitation

References in corpus (5)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Hamiltonian Treatment of the Gravitational Collapse of Thin Shells
• Gravitationally Collapsing Shells in (2+1) Dimensions
• Quantum Collapse of a Small Dust Shell

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• Self-gravitating stellar collapse: explicit geodesics and path integration
• Collapsing Layers on Schwarzschild-Lemaitre Geodesics
• On the existence of deformations and dimensional reduction in wormholes and black holes