Singularity avoidance of charged black holes in loop quantum gravity

DOI10.1007/S10773-012-1248-XzbMATH Open1255.83092arXiv1207.0423OpenAlexW2021863673MaRDI QIDQ1930580

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Publication date: 11 January 2013

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Abstract: Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordstr"{o}m 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 $Qightarrow0$. 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.

Full work available at URL: https://arxiv.org/abs/1207.0423

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