Loop quantization of spherically symmetric midi-superspaces

Abstract

We quantize the exterior of spherically symmetric vacuum space-times using a midi-superspace reduction within the Ashtekar new variables. Through a partial gauge fixing we eliminate the diffeomorphism constraint and are left with a Hamiltonian constraint that is first class. We complete the quantization in the loop representation. We also use the model to discuss the issues that will arise in more general contexts in the ``uniform discretization'' approach to the dynamics.

18 pages, RevTex, no figures, some typos corrected, published version, for some reason a series of figures were incorrectly added to the previous version

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• Phenomenological loop quantum geometry of the Schwarzschild black hole
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• Holography from loop quantum gravity
• Anisotropic Structures and Wormholes with Loop Quantum Gravity Holonomy Corrections
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• Testing general covariance in effective models motivated by Loop Quantum Gravity
• Pulsation of black holes
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