Penetrating the horizon of a hydrodynamic white hole

TL;DR

The paper investigates a hydrodynamic white-hole horizon formed by a circular hydraulic jump in a radially outflowing shallow-water system. By deriving height-averaged equations with viscosity and surface tension, it identifies the horizon at $v_0^2= g h_0$ and analyzes how surface tension perturbs the jump and enables tunnelling of analogue Hawking quanta, yielding a horizon-penetration amplitude governed by a Hawking temperature $T_H$ and a surface-tension correction frequency $\Omega$. A linear perturbation framework reveals an emergent metric and a dispersion relation that capture both the barrier effect of the horizon and the possibility of quantum-like tunnelling, with capillarity capping blue-shift near the horizon. The results highlight the distinct roles of viscosity and surface tension in fluid analogue gravity and suggest experimental routes to probe Hawking-like phenomena in capillary-affected, viscous shallow flows.

Abstract

In a shallow-water radial outflow the horizon of a hydrodynamic white hole coincides with a standing circular hydraulic jump. The jump, caused by viscosity, makes the horizon visible as a circular front, standing as a barrier against the entry of waves within its circumference. The blocking of waves causes a pile-up at the horizon of the white hole, for which surface tension is mainly responsible. Conversely, it is also because of surface tension that the waves can penetrate the barrier. The penetrating waves (analogue Hawking quanta) tunnel through the barrier with a decaying amplitude, but a large-amplitude instability about the horizon is possible.