Group quantization of the black hole minisuperspace
Abstract
The emergence of nontrivial symmetries for black holes minisuperspaces has been recently pointed out. These Noether symmetries possess nonnull charges and hence map physical solutions to different ones. The symmetry group is isomorphic to the finitedimensional Poincaré 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.
 Publication:

Physical Review D
 Pub Date:
 June 2022
 DOI:
 10.1103/PhysRevD.105.126003
 arXiv:
 arXiv:2110.13756
 Bibcode:
 2022PhRvD.105l6003S
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 22 pages + 4 pages of appendix, 2 figures