Black Hole Quasibound States from a Draining Bathtub Vortex Flow

Abstract

Quasinormal modes are a set of damped resonances that describe how an excited open system is driven back to equilibrium. In gravitational physics these modes characterize the ringdown of a perturbed black hole, e.g., following a binary black hole merger. A careful analysis of the ringdown spectrum reveals the properties of the black hole, such as its angular momentum and mass. In more complex gravitational systems, the spectrum might depend on more parameters and hence allows us to search for new physics. We present a hydrodynamic analog of a rotating black hole that illustrates how the presence of extra structure affects the quasinormal mode spectrum. The analogy is obtained by considering wave scattering on a draining bathtub vortex flow. We show that due to vorticity of the background flow, the resulting field theory corresponds to a scalar field on an effective curved spacetime which acquires a local mass in the vortex core. The obtained quasinormal mode spectrum exhibits long-lived trapped modes, commonly known as quasibound states. Our findings can be tested in future experiments building upon recent successful implementations of analog rotating black holes.

Synchronized stationary clouds in a static fluid

“…[13] (see also Ref. [36], which shows that non-zero vorticity can act as an effective mass term, thus allowing quasibound states to appear in vortex flows). For superradiance, the presence of an event horizon is not mandatory [7,[37][38][39]: it can be replaced by any dissipative material, as in the case of Zel'dovich's cylinder that scatters electromagnetic waves [40] or in the case of a rotating cylinder that dissipates the energy of water waves [41].…”

Analogy between freezing lakes and the cosmic radiation era

“…Specifically, factors such as the presence/absence of impurities in the water and their nature and concentration, the atmospheric temperature and its variation in time, the temperature at the bottom of the "lake" (in practice, a deep tank), the lack of winds, and the depth of the "lake" can all be controlled in a laboratory setting. The equipment necessary to conduct an analogue gravity experiment bsed on the physics of water is common in cold laboratories studying snow and ice, while the equipment required is not sophisticated in comparison with that used in conventional analogue gravity in which black holes, cosmological spacetimes, and curved space phenomena such as Hawking radiation, su-perradiance, and false vacuum decay require the use of Bose-Einstein condensates [22][23][24][25]61], ultracold atoms [62], optical systems [63,64], or at least very finely controlled water flows and vortices (e.g., [65][66][67][68]). Likewise, the experimental study of the analogy between freezing lakes and cosmology would require a much simpler laboratory setting than it would be necessary to study the analogy between cosmology and large geological systems such as glaciers and beaches, which also exhibit analogies with cosmology [26,27].…”

Towards a Gordon form of the Kerr spacetime

“…Indeed the Gordon form, (or something conformal to the Gordon form), generically describes the acoustic metric experienced by a linearised perturbation on a relativistic fluid [22,32]. That one might want vorticity in analogue systems is clear from references [37,38,39,40,41,42,43,44]. Very often, however, in theoretical analyses of these analogue systems the inclusion of vorticity is tricky [45] -most typically the four velocity of the fluid is by construction hypersurface orthogonal (implying that it can be written as being proportional to the gradient of some scalar function) and as such -by the Frobenius theorem -it is vorticity free (in the relativistic sense that V ∧ dV = 0).…”