Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole

TL;DR

This paper experimentally demonstrates that the circular hydraulic jump acts as a hydrodynamic white hole, illustrating a gravitational analogy with implications for Hawking radiation and transplanckian effects.

Contribution

It provides the first experimental evidence of the white hole analogy in a circular hydraulic jump and explores its theoretical and physical implications.

Findings

Measured Mach cone angles in the inner flow region.

Confirmed the white hole horizon as a saddle-node bifurcation.

Identified superluminal dispersion relation of surface waves.

Abstract

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time-reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasise the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a "superluminal" dispersion relation, i.e., that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible "transplanckian distortion" of black/white holes.