Black Hole Bomb in a Bathtub: When Vortex Sloshing Whispers Cosmic Physics

Forum topic · 二一 · 2026-05-01

Summary

A new theoretical study (arXiv:2511.05351, Sam Patrick et al., King's College London, University of Nottingham, UFABC, Perimeter Institute) analyzes what happens when the 'black hole bomb' instability — first proposed by Press and Teukolsky in 1972 — is realized in a tabletop analogue gravity experiment. Building on the 2017 Nature Physics observation of rotational superradiance in Weinfurtner's draining-vortex water tank, the authors examine a non-draining Rankine vortex confined in a finite cylindrical container using a variational framework. They reveal a sharp dichotomy: at low circulation, surface sloshing is an instability of the vorticity field unrelated to black hole physics; at high circulation, where fluid is expelled from the core forming a hollow core vortex, the destabilizing mechanism coincides exactly with the black hole bomb — superradiant amplification of waves trapped between ergoregion and container walls. The work also reframes the rotating-polygons instability and provides experimental guidance for superfluid helium-4 quantum vortex experiments seeking cleaner superradiance signatures, precisely delineating the boundaries of analogue gravity.

> *arXiv:2511.05351* | Sam Patrick et al. | King's College London, University of Nottingham, UFABC, Perimeter Institute

Key points

Background — analogue gravity: Since Bill Unruh's 1981 insight, surface waves on a draining water vortex obey equations nearly identical to wave propagation in curved spacetime: the region where flow speed exceeds wave speed corresponds to a black hole event horizon, and the outer rotationally-dominated region corresponds to a rotating black hole's ergoregion. Silke Weinfurtner's "giant bathtub" at Nottingham is the field's flagship experiment.
The theory chain: Penrose (1971) showed energy can be extracted from a rotating black hole's ergoregion; Zel'dovich (1971) proved waves satisfying $0 < \omega < m\Omega$ are amplified by any rotating absorber (rotational superradiance); Press & Teukolsky (1972) showed that combining superradiance with a mirror yields exponential energy growth — the black hole bomb. For massive bosonic fields, the mass term acts as a natural mirror, producing superradiant instabilities.
Prior experiment: In 2017, Weinfurtner's team directly observed superradiance in a water tank — scattered co-rotating waves exited with larger amplitude than they entered.

What the new paper does

The study analyzes a non-draining Rankine vortex (solid-body rotation inside radius $$a$$ , potential-flow decay outside) confined in a finite cylindrical container, in the shallow-water, inviscid limit, using a variational framework that tracks the energy budget of the instability:

1. Energy of vorticity perturbations (distortion of the vortex core's rotation) 2. Energy of irrotational perturbations (free-surface waves) 3. Coupling terms between them

Key findings

Two distinct instability regimes, governed by circulation:
Low circulation: sloshing stems from an instability of the vorticity field itself — vorticity lines twist and resonate. This mechanism is *unrelated* to superradiance.
High circulation: the core is expelling fluid, forming a hollow core. Here the destabilizing mechanism coincides with the black hole bomb: waves gain negative energy inside the ergoregion and are amplified, bouncing between the center and the container walls.

As the authors state: *"At low circulation, the sloshing corresponds to an instability of the vorticity field, whereas at high circulation where fluid is expelled from the vortex core, the destabilising mechanism coincides with that of the black hole bomb."*

Rotating polygons reframed: The famous rotating-polygons instability (Jansson et al. 2006; earlier explained by Tophøj et al. 2013 as gravity–centrifugal wave resonance) is decomposed into competing vorticity and irrotational contributions; at high circulation its mathematical structure closely mirrors the superradiant instability.
Diagnostic tool: The variational energy budget quantifies *where the analogy holds* — a practical check before claiming a tabletop system simulates black hole physics.
Experimental guidance: Hollow-core vortices are the optimal platform for observing black-hole-bomb-like instabilities. This directly informs ongoing superfluid helium-4 quantum vortex experiments (e.g., Švančara et al., *Nature* 2024), which may yield cleaner superradiant instability signals.

Why it matters

The work responds to a common criticism of analogue gravity — that water waves are not gravity waves — by precisely delineating the boundary of validity of the analogy: at low circulation the sloshing is pure fluid dynamics; only at high circulation does the mathematics genuinely capture superradiant physics, in a controllable, repeatable tabletop setting.