Quantum collapse of a small dust shell

A. Corichi, G. Cruz-Pacheco, A. Minzoni, P. Padilla, M. Rosenbaum, M. P. Ryan, N. F. Smyth, T. Vukasinac

Resultado de la investigación: Contribución a una revistaArtículo

13 Citas (Scopus)

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 originalInglés
Número de artículo064006
Páginas (desde-hasta)640061-6400613
Número de páginas5760553
PublicaciónPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volumen65
N.º6
EstadoPublicada - 15 mar 2002

Huella dactilar

quantum mechanics
dust
encounters
orbits
momentum
formulations
operators
radii

Citar esto

Corichi, A., Cruz-Pacheco, G., Minzoni, A., Padilla, P., Rosenbaum, M., Ryan, M. P., ... Vukasinac, T. (2002). Quantum collapse of a small dust shell. Physical Review D - Particles, Fields, Gravitation and Cosmology, 65(6), 640061-6400613. [064006].
Corichi, A. ; Cruz-Pacheco, G. ; Minzoni, A. ; Padilla, P. ; Rosenbaum, M. ; Ryan, M. P. ; Smyth, N. F. ; Vukasinac, T. / Quantum collapse of a small dust shell. En: Physical Review D - Particles, Fields, Gravitation and Cosmology. 2002 ; Vol. 65, N.º 6. pp. 640061-6400613.
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Corichi, A, Cruz-Pacheco, G, Minzoni, A, Padilla, P, Rosenbaum, M, Ryan, MP, Smyth, NF & Vukasinac, T 2002, 'Quantum collapse of a small dust shell', 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.

En: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 65, N.º 6, 064006, 15.03.2002, p. 640061-6400613.

Resultado de la investigación: Contribución a una revistaArtículo

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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.

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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.

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Corichi A, Cruz-Pacheco G, Minzoni A, Padilla P, Rosenbaum M, Ryan MP y otros. Quantum collapse of a small dust shell. Physical Review D - Particles, Fields, Gravitation and Cosmology. 2002 mar 15;65(6):640061-6400613. 064006.