Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

Abstract

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordström black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case $M^2>Q^2$. This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Swcharzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit $Q\to 0$. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.

To be appeared in International Journal of Theoretical Physics

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• Loop Quantum Cosmology
• Quantum geometry and the Schwarzschild singularity
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Inflation from Quantum Geometry
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• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
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Cited by in corpus (4)

• Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors
• Minisuperspace Canonical Quantization of the Reissner-Nordstrom Black Hole via Conditional Symmetries
• Loop Quantum Corrected Einstein Yang-Mills Black Holes
• Quantization of Reissner-Nordström Black Holes and Their Non-Singular Quantum Behavior