Quantum dynamics of the black hole interior in LQC

TL;DR

This paper uses unimodular gravity to analyze the full quantum dynamics of black hole interiors in loop quantum cosmology, showing how states evolve through singularities with potential to clarify regularization issues.

Contribution

It introduces a novel approach using unimodular gravity to study quantum black hole interiors, enabling Schrödinger evolution and detailed state analysis.

Findings

States evolve through singularities while remaining sharply peaked

Provides a simplified framework for full quantum dynamics analysis

Potential to address regularization ambiguities in LQC

Abstract

It has been suggested that the homogeneous black hole interior spacetime, when quantized following the techniques of loop quantum cosmology, has a resolved singularity replaced by a black-to-white hole transition. This result has however been derived so far only using effective classical evolution equations, and depends on details of the so-called polymerization scheme for the Hamiltonian constraint. Here we propose to use the unimodular formulation of general relativity to study the full quantum dynamics of this mini-superspace model. When applied to such cosmological models, unimodular gravity has the advantage of trivializing the problem of time by providing a true Hamiltonian which follows a Schr\"odinger evolution equation. By choosing variables adapted to this setup, we show how to write semi-classical states agreeing with that of the Wheeler-DeWitt theory at late times, and how in loop quantum cosmology they evolve through the would-be singularity while remaining sharply peaked. This provides a very simple setup for the study of the full quantum dynamics of these models, which can hopefully serve to tame regularization ambiguities.