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

References in corpus (3)

• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Quantum nature of cosmological bounces