Group quantization of the black hole minisuperspace

TL;DR

This paper explores the symmetry structure of black hole minisuperspaces, leading to a quantum theory that predicts a continuous mass spectrum and replaces singularities with horizons, inspired by loop quantum cosmology.

Contribution

It introduces a group quantization approach based on the Poincaré symmetry of black hole minisuperspaces, providing a new framework for quantum black hole models.

Findings

Symmetry group is isomorphic to ISO(2,1).

Mass spectrum is continuous.

Singularity replaced by a Killing horizon.

Abstract

The emergence of nontrivial symmetries for black holes minisuperspaces has been recently pointed out. These Noether symmetries possess non-null charges and hence map physical solutions to different ones. The symmetry group is isomorphic to the finite-dimensional Poincar\'e group ISO(2,1), whose irreducible representations are well known. This structure is used to build a consistent quantum theory of black hole minisuperspace. This has, among other consequences, the striking consequence of implying a continuous spectrum for the mass operator. Following loop quantum cosmology, we obtain a regularization scheme compatible with the symmetry structure. It is possible to study the evolution of coherent states following the classical trajectories in the low curvature regime. We show that this produces an effective metric where the singularity is replaced by a Killing horizon merging two asymptotically flat regions. The quantum correction comes from a fundamental discreteness of spacetime, and the uncertainty on the energy of the system. Remarkably, the effective evolution of semiclassical states is described by an effective Hamiltonian, related to the original one through a canonical transformation.