Speaker
Description
In this work, we examine the quantum properties of a Kantowski-Sachs minisuperspace through the lense of Dirac quantization and relational evolution. The relational dynamic is obtained thanks to the use of quantum clocks, which are built from one of the two degrees of freedom of the metric. Gauge-invariant extension of gauge-dependent observables are built relationally with respect to the quantum clocks, and their matrix elements are considered in order to give physical insights about the interior of Black Holes. The observables considered are both the expansion parameter for radial null geodesics and the Kretschmann scalar. In particular, this model shows how both of these quantities are always finite for any instant of quantum and relational time. Therefore, we claim that in a fully quantum and relational model of spacetime, even with the use of the standard Schrodinger continuous representation, the singularity is resolved. Further analysis, involving the computations of the matrix elements of the proper area of 2D-spheres, clearly show that a bounce happens at the singularity, leading to a Black-to-White Hole transition. All these results are obtained without any use of loop variables or polymer quantization, and yet they lead to results that are very similar to the ones obtained in Loop Quantum Cosmology. This model also opens new paths for a connection between the Quantum Reference Frame's framework and Quantum Gravity.