Collapsing shells and black holes: a quantum analysis

Abstract

The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. The encountered properties are investigated making use of the Israel junction conditions on the shell, considering that it is the boundary between two spherically symmetric spacetimes. Using this method, and considering two different Kantowski-Sachs spacetimes as a representation for the Schwarzschild spacetime, the relevant quantities on the shell are computed, such as its stress-energy tensor and the action for the whole spacetime. From the obtained action, the Wheeler-deWitt equation is deduced in order to provide the quantum framework for the system. Solutions for the wavefunction of the system are found on both the commutative and NC scenarios. It is shown that, on the commutative version, the wave function has a purely oscillatory behavior in the interior of the shell. In the NC setting, it is shown that the wavefunction vanishes at the singularity, as well as, at the event horizon of the black hole.

Spin‐Spacetime Censorship

“…This noncommutativity implies the following uncertainty relations (see, e.g., refs. [79,80] ) Δx 𝜇 Δx 𝜈 ≥ 1 2 |Θ 𝜇𝜈 |. We thus see that, similar to measurements of a quantum electromagnetic field, one has to choose a measurement basis, thus rendering the system contextual.…”

An exact, coordinate independent classical firewall transformation

“…A common simplified model is a spherically symmetric distribution of matter collapsing or expanding in a Schwarzschild black hole background, e.g. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For example, quantization procedures for a single shell collapse demonstrate completely unitary evolution as the shell collapses and subsequently bounces back outwards after a long black-hole-like epoch [10,11].…”

Phase-space elementary information content of confined Dirac spinors

“…Enlarging the access to elementary information features of physical systems without affecting the predictive power of quantum mechanics, the Wigner phase-space representation [1][2][3][4] of quantum mechanics has currently shed some light on the investigation of the frontiers between classical and quantum descriptions of Nature [5][6][7][8]. Besides its ferramental pragmatic utility demanded by optical quantum mechanics [9], in the theoretical front, the Wigner quantum mechanics has also worked as a robust support for the non-commutative quantum mechanics [10][11][12][13][14][15][16][17][18][19], for the description of the flux of quantum information in the phase-space [20][21][22][23] and, more generically, for probing quantumness and classicality for a relevant set of anharmonic quantum systems [22,24,25] as well as for quantitative modeling beyond the quantum physical framework [26].…”