Negative frequencies and negative norms in analogue Hawking radiation systems

TL;DR

This paper examines the roles of negative frequencies and norms in Hawking radiation within astrophysical and analogue systems, emphasizing the importance of the static horizon frame for understanding particle creation.

Contribution

It clarifies the relationship between negative frequencies and norms and their impact on Hawking radiation in various analogue systems, proposing the static horizon frame as the natural context.

Findings

The sign of the norm can be aligned with the Doppler-shifted frequency in the static horizon frame.

Analysis of water waves, BECs, polaritons, and optical fibers as analogue systems.

Clarification of the role of negative frequencies and norms in Hawking radiation.

Abstract

In this work, we study the core concepts of Hawking radiation in the astrophysical and analogue systems. We focus on the definitions of negative frequencies and negative norms: their relationship and their role in the particle creation process of the Hawking effect. We characterize the dispersion relation by the signs of the frequency and the norm. We conclude that the most natural frame for studying the Hawking effect is in the frame in which the horizon is static, where the sign of the norm can be made equal to the sign of the Doppler-shifted frequency in that frame. We use as examples the four most successful experimental analogue systems: water waves, Bose-Einstein condensates, polaritons fluids, and optical fibers.