Vortex geometry for the equatorial slice of the Kerr black hole

Details Vortex geometry for the equatorial slice of the Kerr black hole Vortex geometry for the equatorial slice of the Kerr black hole

2004-09-03

arxiv.org/abs/gr-qc/0409014v2

Class.Quant.Grav. 22 (2005) 2493-2510

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

V1: 24 pages, 5 figures (some use of colour); V2: 21 pages, 5 figures, uses iopart.cls Changes of style and emphasis, no major

Scientific paper

10.1088/0264-9381/22/12/011

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 situation 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 briefly 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.

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