Abstract
We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains semi-classical states that approximate general relativity coupled to an effective anisotropic fluid. The singularity is eliminated and the space-time can be continued into a white hole space-time. This is similar to previously considered scenarios based on a loop quantum gravity quantization.
Highlights
In a previous paper (Gambini et al, 2020a) we studied an improved quantization for spherically symmetric loop quantum gravity
As we discussed in our previous papers, the quantum theory has additional observables to the ones encountered in classical treatments (Kastrup and Thiemann, 1994; Kuchar, 1994) which are the ADM mass and the time at infinity. These emerge from the discrete nature of the spin network treatment and are associated with the ki’s, which in turn are associated with the value of the areas of the spheres of symmetry connected with each vertex of the spin network
The effective geometries that one can derive in this theory are uniquely determined by the semiclassical physical state and the observables that represent the components of the metric
Summary
In a previous paper (Gambini et al, 2020a) we studied an improved quantization for spherically symmetric loop quantum gravity. Earlier work (Gambini and Pullin, 2013; Gambini et al, 2014; Gambini et al, 2020b) had considered a constant polymerization parameter, to the “μ0” quantization scheme in loop quantum cosmology, whereas the improved quantization is similar to the “μ” quantization scheme (Ashtekar and Singh, 2011). The space-time continues into a white hole geometry, like in Ref.
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