Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

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...

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Bibliographic Details
Published in:arXiv.org 2012-07
Main Authors: Mojtaba Taslimi Tehrani, Heydari, Hoshang
Format: Article
Language:English
Subjects:
Avoidance
Black holes
Curvature
Mathematical analysis
Operators (mathematics)
Quantum gravity
Upper bounds
Online Access:Get full text
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Summary: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 \(Q \rightarrow 0\). 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1207.0423