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arXiv · 2010.07056

Quantum dynamics of the black hole interior in LQC

Francesco Sartini·Marc Geiller
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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.

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Francesco Sartini, Marc Geiller. 2020-10-14. Quantum dynamics of the black hole interior in LQC. https://doi.org/10.1103/physrevd.103.066014

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