Some aspects of dispersive horizons: lessons from surface waves

TL;DR

This paper investigates how surface wave dispersion and surface tension affect the behavior of analogue black/white-hole horizons in fluid flows, revealing phenomena like horizon penetration, dispersive cusps, and high-frequency corrections relevant to analogue gravity models.

Contribution

It introduces the role of surface tension-induced blue horizons and dispersive cusps in hydrodynamic horizons, expanding understanding of wave interactions in analogue gravity systems.

Findings

Penetration across horizons due to blue horizon interaction.

Dispersive cusp causes horizons to disappear at high frequencies.

High-frequency superluminal corrections are likely universal in analogue systems.

Abstract

Hydrodynamic surface waves propagating on a moving background flow experience an effective curved space-time. We discuss experiments with gravity waves and capillary-gravity waves in which we study hydrodynamic black/white-hole horizons and the possibility of penetrating across them. Such possibility of penetration is due to the interaction with an additional "blue" horizon, which results from the inclusion of surface tension in the low-frequency gravity-wave theory. This interaction leads to a dispersive cusp beyond which both horizons completely disappear. We speculate the appearance of high-frequency "superluminal" corrections to be a universal characteristic of analogue gravity systems, and discuss their relevance for the trans-Planckian problem. We also discuss the role of Airy interference in hybridising the incoming waves with the flowing background (the effective spacetime) and blurring the position of the black/white-hole horizon.