Some considerations on BEC analogue black holes

TL;DR

The paper surveys how Hawking radiation can be studied in Bose-Einstein condensate analogues, focusing on the acoustic metric and the Bogoliubov–de Gennes description of phonons near a sonic horizon. It analyzes the role of dispersion, gray-body factors, and limiting profiles in shaping the emission spectrum, showing where the gravitational analogy faithfully reproduces thermal radiation and where it breaks down due to short-distance physics (e.g., step profiles yielding a finite cutoff $\omega_{max} \sim \xi^{-1}$). It also highlights correlations as robust signatures, including a characteristic density–density peak, and cites experimental evidence of Hawking-like phonon pairs (e.g., Steinhauer), underscoring the practical potential of analogue gravity experiments. The work clarifies how transplanckian concerns are addressed by dispersion in BEC systems and emphasizes the interplay between theory and experiment in validating Hawking physics in laboratory settings.

Abstract

In this paper, dedicated to the memory of A. Aurilia, we will review some basic features of Hawking's black hole radiation and compare them with the corresponding ones present in Bose-Einstein condensate analogue black holes.

Figures (13)

• Figure 1: For the Hawking particle, the local frequency close to the horizon is exponentially amplified with respect to its frequency measured at infinity and the corresponding energy becomes transplanckian.
• Figure 2: Schematic representation of an acoustic black hole.
• Figure 3: Black hole formed by gravitational collapse.
• Figure 4: BEC dispersion relation in the subsonic region.
• Figure 5: BEC dispersion relation in the supersonic region.