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Effective geometries and generalized uncertainty principle corrections to the Bekenstein-Hawking entropy

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 non-linear electrodynamics, which resembles previously studied regular black-hole solutions.