A Vortex's Silent Patch Reveals Its Speed ⚡ экспресс
A formalism for acoustic ray transport is constructed, resolved by impact parameter in the spacetime of a rotating drain (the 'bathtub vortex' model). Ray geometry is separated from source and detector characteristics: acoustic redshift, transport convention, emissivity, velocity field, and source-screen mapping are accounted for. The geometric capture interval yields two clean observables: the shadow centroid, shifting linearly with circulation, and the shadow width, growing monotonically. Transport calculations reveal that rotation induces a left-right redshift tilt and a branch-dependent flux imbalance, while the total flux is a degenerate indicator. Most informative are differential quantities: shadow centroid, branch flux asymmetry, peak asymmetry, left-right redshift asymmetry, and global redshift contrast. The influence of transport convention, azimuthal emissivity, choice of left-right split, finite resolution, as well as physical limitations—dispersion, viscosity, and finite-depth corrections—is discussed.
In a water vortex swirling toward the drain, the flow speed near the center can exceed the speed of sound. Sound gets trapped: waves cannot escape back, forming a silent region—a sound shadow. Half a century ago, William Unruh realized that this is an exact copy of a black hole, but for sound instead of light. If the vortex also rotates, the shadow shifts and stretches in the direction of rotation. By measuring the shadow's position relative to the center, you can directly calculate the rotation speed. Moreover, rotation changes the pitch of sound on the sides of the vortex: on one side it becomes lower (like a receding siren), on the other—higher. Just compare these two tones, and the difference will reveal the rotation more accurately than any direct measurement. This approach, transferred from astrophysics to laboratory water models, helps study black holes without telescopes. The most surprising thing: the equations for a kitchen vortex and for a giant hole at the center of a galaxy are the same, only the 'trapped' object differs: sound or light. This simple fact allows us to literally touch the mysteries of curved spacetime in our own lab.
🎯 For real black holes, rotation also distorts the shadow: it becomes egg-shaped and shifts in the direction of rotation—just like in our water model.
🎬 In the movie Interstellar, the black hole Gargantua appears with an asymmetric shadow and a bright ring—exactly like our sound vortex, only for light.