Formation dynamics of black- and white-hole horizons in an analogue gravity model

TL;DR

This paper studies how sonic horizons form in a one-dimensional Bose gas, revealing conditions for black-hole-like horizons and showing limitations of semiclassical models in capturing these dynamics.

Contribution

It demonstrates the formation of sonic horizons in a Bose gas using exact solutions and compares these with semiclassical predictions, highlighting their limitations.

Findings

Sonic horizons form when switching on a step potential, depending on initial flow velocity.

No evidence of isolated white-hole horizons in dynamical simulations.

Semiclassical Gross-Pitaevskii dynamics align with exact solutions only in fully subsonic flows.

Abstract

We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks-Girardeau gas) we show that, by switching on a step potential, either a sonic (black-hole-like) horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated white-hole horizon, although a stable stationary solution of the dynamical equations with those properties is analytically found. Moreover, we show that the semiclassical dynamics, based on the Gross-Pitaevskii equation, conforms to the exact solution only in the case of fully subsonic flows while a stationary solution exhibiting a supersonic transition is never reached dynamically.