Spherically Symmetric Quantum Geometry: States and Basic Operators

Abstract

The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory aspects arise. A comparison between a reduced quantization and a derivation of the model from the full theory is presented in detail, with an emphasis on the resulting quantum representation. Similar concepts for Einstein-Rosen waves are discussed briefly.

26 pages

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• Quantum geometry and the Schwarzschild singularity
• Black hole evaporation: A paradigm
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• Loop quantum black hole
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• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model