Quantum space-time of a charged black hole

Abstract

We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie algebra. We complete the Dirac quantization procedure using loop quantum gravity techniques. We present explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. The resulting quantum space-times resolve the singularity present in the classical theory inside charged black holes and allows to extend the space-time through where the singularity used to be into new regions. We show that quantum discreteness of space-time may also play a role in stabilizing the Cauchy horizons, though back reaction calculations are needed to confirm this point.

arXiv comment6 pages, RevTex, one figure

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• Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors
• Construction of quantum Dirac observables and the emergence of WKB time
• Quantum evolution of black hole initial data sets: Foundations
• Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections
• Quantum self-gravitating collapsing matter in a quantum geometry
• Singularity resolution by holonomy corrections: Spherical charged black holes in cosmological backgrounds
• Brief review on black hole loop quantization
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• Measuring the last burst of non-singular black holes
• Classical axisymmetric gravity in real Ashtekar variables
• Quantum geometry and black holes
• Non-singular naked solutions in quantum spacetime
• Covariant effective spacetimes of spherically symmetric electrovacuum with a cosmological constant
• Thermodynamics of effective loop quantum black holes
• Particles as superoscillations of spacetime with a nonlocal metric?
• Quantum kicks near a Cauchy horizon