Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon

TL;DR

The paper clarifies the distinction between Hawking and Unruh effects, proposing an interpretation and formula to separate them, and discusses conditions for a free-falling detector to cross a black hole horizon smoothly.

Contribution

It introduces an inconsistency-free interpretation and an analytic formula to distinguish Hawking and Unruh effects, aiding understanding of detector experiences near black holes.

Findings

A new interpretation clarifies the separation of Hawking and Unruh effects.

An analytic formula is derived to distinguish the two effects.

Crossing the horizon at low velocities leads to high-energy effects.

Abstract

When analyzing the perception of Hawking radiation by different observers, the Hawking effect becomes mixed with the Unruh effect. The separation of both effects is not always clear in the literature. Here we propose an inconsistency-free interpretation of what constitutes a Hawking effect and what an Unruh effect. An appropriate interpretation is important in order to elucidate what sort of effects a detector might experience depending on its trajectory and the state of the quantum field. Under simplifying assumptions we introduce an analytic formula that separates these two effects. Armed with the previous interpretation we argue that for a free-falling detector to cross the horizon without experiencing high-energy effects, it is necessary that the horizon crossing is not attempted at low velocities.