Short-distance Cut-off from the Quantum Dynamics of Fields in a Black Hole Spacetime

We stress the strongly observer-dependent nature of the fine-grained black hole entropy as computed by usual methods. From the point of view of a fiducial observer, the 1-loop renormalized energy-momentum tensor diverges at the horizon. Considering, more consistently, the computation of the black hole entropy in the back-reaction-corrected curved background an ultraviolet cut-off, needed to regularize the entropy, naturally araises. Examples of the classical dynamics of test particles, strings and relativistic membranes in the corrected metric are also given to complete the picture.