# Unruh Acceleration Radiation Revisited

## TL;DR

This paper explores how accelerated atoms and those falling into black holes emit radiation resembling Hawking radiation, providing insights into the Unruh effect, black hole physics, and the equivalence principle.

## Contribution

It revisits Unruh radiation, linking it to Hawking radiation and black hole physics, with a novel analysis of acceleration radiation under specific initial conditions.

## Key findings

- Atoms emit Unruh radiation when accelerated in vacuum
- Falling atoms into black holes emit radiation similar to Hawking radiation
- The Unruh temperature is derived using the KMS condition with a new perspective

## Abstract

When ground-state atoms are accelerated and the field with which they interact is in its normal vacuum state, the atoms detect Unruh radiation. We show that atoms falling into a black hole emit acceleration radiation which, under appropriate initial conditions (Boulware vacuum), has an energy spectrum which looks much like Hawking radiation. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity. The Unruh temperature can also be obtained by using the Kubo--Martin--Schwinger (KMS) periodicity of the two-point thermal correlation function, for a system undergoing uniform acceleration; as with much of the material in this paper, this known result is obtained with a twist.