### Resumen

The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Hájíček and Kuchař. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self-adjoint momentum operator in the space of the shell motion which is confined to a half-line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has a very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

Idioma original | Inglés |
---|---|

Número de artículo | 064006 |

Páginas (desde-hasta) | 640061-6400613 |

Número de páginas | 5760553 |

Publicación | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volumen | 65 |

N.º | 6 |

Estado | Publicada - 15 mar 2002 |

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*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*65*(6), 640061-6400613. [064006].

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 65, n.º 6, 064006, pp. 640061-6400613.

**Quantum collapse of a small dust shell.** / Corichi, A.; Cruz-Pacheco, G.; Minzoni, A.; Padilla, P.; Rosenbaum, M.; Ryan, M. P.; Smyth, N. F.; Vukasinac, T.

Resultado de la investigación: Contribución a una revista › Artículo

TY - JOUR

T1 - Quantum collapse of a small dust shell

AU - Corichi, A.

AU - Cruz-Pacheco, G.

AU - Minzoni, A.

AU - Padilla, P.

AU - Rosenbaum, M.

AU - Ryan, M. P.

AU - Smyth, N. F.

AU - Vukasinac, T.

PY - 2002/3/15

Y1 - 2002/3/15

N2 - The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Hájíček and Kuchař. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self-adjoint momentum operator in the space of the shell motion which is confined to a half-line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has a very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

AB - The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Hájíček and Kuchař. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self-adjoint momentum operator in the space of the shell motion which is confined to a half-line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has a very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

UR - http://www.scopus.com/inward/record.url?scp=0037088194&partnerID=8YFLogxK

M3 - Artículo

AN - SCOPUS:0037088194

VL - 65

SP - 640061

EP - 6400613

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 6

M1 - 064006

ER -