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

TL;DR

This paper explores the observer-dependent nature of black hole entropy, highlighting the need for an ultraviolet cut-off in the back-reaction-corrected spacetime and examining classical dynamics in this context.

Contribution

It introduces a natural ultraviolet cut-off arising from back-reaction effects for regularizing black hole entropy calculations.

Findings

The energy-momentum tensor diverges at the horizon for a fiducial observer.

A natural ultraviolet cut-off emerges from back-reaction considerations.

Classical dynamics of particles, strings, and membranes are analyzed in the corrected metric.

Abstract

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.