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Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

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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-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 Schwarzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit Q→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.

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Notes

  1. We are following Rovelli[1]’s notation in which indices μ,ν,… denote space-time, i,j,… 3-space and a,b,…ℝ3 indices.

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Authors and Affiliations

  1. Department of Physics, Stockholm University, 10691, Stockholm, Sweden

    Mojtaba Taslimi Tehrani & Hoshang Heydari

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  1. Mojtaba Taslimi Tehrani
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  2. Hoshang Heydari
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Correspondence to Mojtaba Taslimi Tehrani.

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The work was supported by the Swedish Research Council (VR).

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Taslimi Tehrani, M., Heydari, H. Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity. Int J Theor Phys 51, 3614–3626 (2012). https://doi.org/10.1007/s10773-012-1248-x

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  • DOI: https://doi.org/10.1007/s10773-012-1248-x

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