Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-09-17
Phys.Rev. D65 (2002) 064006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, 8 figures, Revtex4 file
Scientific paper
10.1103/PhysRevD.65.064006
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 H\'aj{\'\i}\v{c}ek and Kucha\v{r}. 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 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.
Corichi Alejandro
Cruz G.
Minzoni Antonmaria A.
Padilla P.
Rosenbaum Marcos
No associations
LandOfFree
Quantum Collapse of a Small Dust Shell does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Collapse of a Small Dust Shell, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Collapse of a Small Dust Shell will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-424911