Stability analysis of sonic horizons in Bose-Einstein condensates

TL;DR

This paper investigates the linear stability of various sonic horizon configurations in Bose-Einstein condensates, revealing how boundary conditions influence their stability and drawing parallels with gravitational systems.

Contribution

It provides a detailed stability analysis of sonic horizons in BECs under different boundary conditions, highlighting the importance of these conditions in stability outcomes.

Findings

Black hole configurations are stable under standard boundary conditions.

White hole and black hole-white hole configurations can develop instabilities with less stringent boundary conditions.

Boundary conditions significantly affect the stability of sonic horizon configurations.

Abstract

We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational terms. We highlight that the stability of a given configuration, not only depends on its specific geometry, but especially on these boundary conditions. Under boundary conditions directly extrapolated from those in standard General Relativity, black hole configurations, white hole configurations and the combination of both into a black hole--white hole configuration are shown to be stable. However, we show that under other (less stringent) boundary conditions, configurations with a single black hole horizon remain stable, whereas white hole and black hole--white hole configurations develop instabilities associated to the presence of the sonic horizons.