With GUP-modified effective metrics and tuned cutoffs (or tuned GUP parameter), the brick-wall entropy is made to reproduce the Bekenstein-Hawking area law.
Effective geometries and generalized uncertainty principle corrections to the Bekenstein-Hawking entropy
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abstract
In this work we construct several black hole metrics which are consistent with the generalized uncertainty principle logarithmic correction to the Bekenstein-Hawking entropy formula. After preserving the event horizon at the usual position, a singularity at the Planck scale is found. Finally, these geometries are shown to be realized by certain model of nonlinear electrodynamics, which resembles previously studied regular black hole solutions.
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Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
With GUP-modified effective metrics and tuned cutoffs (or tuned GUP parameter), the brick-wall entropy is made to reproduce the Bekenstein-Hawking area law.