Quantum collapse of a self-gravitating thin shell and statistical model of quantum black hole

Xu, Donghui

doi:10.1016/j.physletb.2006.07.063

Cited by 6 publications

(5 citation statements)

References 37 publications

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“…One could also, in principle, imagine that it is preferable to describe the evolution in the external time [14,15], i.e., from the standpoint of the asymptotic observer. Rewriting the constraint in terms of R t , using (13), one gets…”

Section: Classical Thin Shellsmentioning

confidence: 99%

“…On the classical level, the shell has just one degree of freedom and is completely described by its radius, R(t) and its conjugate momentum, P (t). Yet, various versions of it form a rich enough collection of physical systems to describe the final stages of gravitational collapse, Hawking radiation and the formation (or avoidance) of gravitational singularities [12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Collapse of a Thin Shell Revisited

Vaz

2022

Preprint

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There are several possible choices of the time parameter for the canonical description of a self-gravitating thin shell, but quantum thories built on different time parameters lead to unitarily inequivalent descriptions. We compare the quantum collapse of a thin dust shell in two different times viz., the time coordinate in the interior of the shell (originally addressed in [1]) and the time coordinate of the comoving observer (proper time). In each case, we obtain exact solutions to the Wheeler-DeWitt equation requiring only a finite and well behaved U (1) current. The two quantum theories are complementary and each highlights the role played by the Planck mass: stationary states of positive energy in interior time exist only if the shell rest mass in smaller than the Planck mass. In proper time they exist only when the shell rest mass is greater than the Planck mass. In coordinate time there are both scattering states and bound states with a well defined energy spectrum. In the proper time description there are only bound states, whose spectrum we determine.

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Section: Classical Thin Shellsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Collapse of a Thin Shell Revisited

Vaz

2022

Preprint

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“…On the quantum side, this is a rare solvable model which describe a fully quantum interaction between gravity and matter. As such significant attention has been given to the quantum theory [1][2][3][4][5][6]. Perhaps the most influential work in this area is that of Hájíček, Kay and Kuchař [1] where a Wheeler-DeWitt quantization was successfully completed for shells with a rest mass m < 1 (in Planck units).…”

Section: Introductionmentioning

confidence: 99%

Polymer quantization of a self-gravitating thin shell

2016

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We study the quantum mechanics of self-gravitating thin shell collapse by solving the polymerized Wheeler-DeWitt equation. We obtain the energy spectrum and solve the time dependent equation using numerics. In contradistinction to the continuum theory, we are able to consistently quantize the theory for super-Planckian black holes, and find two choices of boundary conditions which conserve energy and probability, as opposed to one in the continuum theory. Another feature unique to the polymer theory is the existence of negative energy stationary states that disappear from the spectrum as the polymer scale goes to zero. In both theories the probability density is positive semidefinite only for the space of positive energy stationary states. Dynamically, we find that an initial Gaussian probability density develops regions of negative probability as the wavepacket approaches R = 0 and bounces. This implies that the bouncing state is a sum of both positive and negative eigenstates.

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mentioning

confidence: 99%

“…The quantum theory of (8) was discussed in detail in [25], so we will first consider the quantum theory of the shell in proper time given in (9). For any two solutions of the wave equation, Φ and Ψ, there is a conserved bilinear current density,…”

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confidence: 99%

Proper time Quantization of a Thin Shell

Vaz

2022

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Time" has different meanings in classical general relativity and in quantum theory. While all choices of a time function yield the same local classical geometries, quantum theories built on different time functions are not unitarily equivalent. This incompatibility is most vivid in model systems for which exact quantum descriptions in different time variables are available. One such system is a spherically symmetric, thin dust shell. In this essay we will compare the quantum theories of the shell built on proper time and on a particular coordinate time. We find wholly incompatible descriptions: whereas the shell quantum mechanics in coordinate time admits no solutions when the mass is greater than the Planck mass, its proper time quantum mechanics only admits solutions when the mass is greater than the Planck mass. The latter is in better agreement with what is expected from observation. We argue that proper time quantization provides a superior approach to the problem of time in canonical quantization.

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Quantum collapse of a self-gravitating thin shell and statistical model of quantum black hole

Cited by 6 publications

References 37 publications

Quantum Collapse of a Thin Shell Revisited

Quantum Collapse of a Thin Shell Revisited

Polymer quantization of a self-gravitating thin shell

Proper time Quantization of a Thin Shell

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