Polymer Quantization of a Self-Gravitating Thin Shell

Understand

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.