Abstract
Here, we present a review about the quantization of spherically-symmetric spacetimes adopting loop quantum gravity techniques. Several models that have been studied so far share similar properties: the resolution of the classical singularity and some of them an intrinsic discretization of the geometry. We also explain the extension to Reissner–Nordström black holes. Besides, we review how quantum test fields on these quantum geometries allow us to study phenomena, like the Casimir effect or Hawking radiation. Finally, we briefly describe a recent proposal that incorporates spherically-symmetric matter, discussing its relevance for the understanding of black hole evolution.
Highlights
Black holes are one of the most fascinating entities in the cosmos
If we look at the previous inner product, there is a natural basis of physical states | M,~kiPhys, where the basic observables are given by M, the mass of the black hole and a new observable without a classical Dirac analogue, defined as: Ô(z)| M,~kiPhys = γ2Pl kInt(nz) | M,~k iPhys recalling that n is the number of vertices and with z ∈ [0, 1] a gauge parameter, and Int(nz) means the integer part of nz
There is no agreement at present in the typical times of black hole evaporation, whether they are long [82] or not [79,80,81]. In this contribution, we have reviewed the recent advances in the loop quantization of spherically-symmetric spacetimes and their application in several aspects of black hole physics, like singularity resolution, black hole formation and interesting phenomena on quantum field theory on quantum spacetimes
Summary
Black holes are one of the most fascinating entities in the cosmos. Some of their properties can be described with Einstein’s theory of gravity in a relatively simple way. The quantization techniques of loop quantum gravity have been successfully applied in many mini- and midi-superspace models [4,5,6] In those cases where the physical sector has been explicitly solved, this quantization program provides a good semiclassical limit reproducing general relativity and a robust resolution of the classical singularity (replaced by a regular region of high curvature) at the deep. We do not know which is the true physical description close to the classical singularity (where general relativity breaks down) or the essential nature of Hawking radiation. In the latter case, it leads to black hole evaporation and eventually to the information loss paradox.
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