Semiclassical approach for the evaporating black hole revisited

TL;DR

This paper revisits the semiclassical analysis of evaporating black holes, clarifying discrepancies in energy density calculations near the horizon and addressing conflicts between recent and traditional results.

Contribution

It provides a revised calculation of free-fall energy density around black holes, highlighting differences from previous studies and resolving existing conflicts.

Findings

Energy density is finite for observers released from rest outside the horizon.

Energy density diverges negatively as the observer starts falling from the horizon.

Revised calculations clarify conflicts in existing literature.

Abstract

A recent calculation shows that the observed energy density in the Unruh state at the future event horizon as seen by a freely falling observer is finite if the observer is released from rest at any positive distance outside the horizon; however, it is getting larger and larger so that it is negatively divergent at the horizon in the limit that the observer starts falling from rest at the horizon, which corresponds to the infinite boost with respect to the freely falling observer at a finite distance from the horizon. In order to resolve some conflicts between the recent calculation and the conventional ones in the well-known literatures, the calculation of the free-fall energy density is revisited and some differences are pointed out.