From Navier-Stokes to Maxwell via Einstein

Understand

We revisit the cutoff surface formulation of fluid-gravity duality in the context of the classical double copy.

• The spacetimes in this fluid-gravity duality are algebraically special, with Petrov type II when the spacetime is four dimensional.
• We find two special classes of fluids whose dual spacetimes exhibit higher algebraic speciality: constant vorticity flows have type D gravity duals, while potential flows map to type N spacetimes.
• Using the Weyl version of the classical double copy, we construct associated single-copy gauge fields for both cases, finding that constant vorticity fluids map to a solenoid gauge field.