Collapsing Shells and Black Holes: a quantum analysis
  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.
