Vortex analogue for the equatorial geometry of the Kerr black hole

The spacetime geometry on the equatorial slice through a Kerr black hole is formally equivalent to the geometry felt by phonons entrained in a rotating fluid vortex. We analyse this example of “analogue gravity” in some detail: First, we find the most general acoustic geometry compatible with the fluid dynamic equations in a collapsing/expanding perfect-fluid line vortex. Second, we demonstrate that there is a suitable choice of coordinates on the equatorial slice through a Kerr black hole that puts it into this vortex form; though it is not possible to put the entire Kerr spacetime into perfect-fluid “acoustic” form. Finally, we discuss the implications of this formal equivalence; both with respect to gaining insight into the Kerr spacetime and with respect to possible vortex-inspired experiments, and indicate ways in which more general analogue spacetimes might be constructed. PACS numbers: 02.40.Ma. 04.20.Cv, 04.20.Gz, 04.70.-s Vortex analogue for the equatorial geometry of the Kerr black hole 2