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We give a correction to the tunneling probability by taking into account the back reaction effect to the metric of the black hole spacetime.
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For a review and a complete list of papers on logarithmic corrections, see
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S.Shankaranarayanan, T.Padmanabhan and K.Srinivasan, Class. Quantum Grav. 19, 2671 (2002)
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T.Pilling, Tunneling Derived from Black Hole Thermodynamics
Cited in the paper.