Vortex geometry for the equatorial slice of the Kerr black hole
Sep, 2004Citations per year
Abstract: (arXiv)
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.Note:
- V1: 24 pages, 5 figures (some use of colour): V2: 21 pages, 5 figures, uses iopart.cls Changes of style and emphasis, no major changes in physics conclusions. This version accepted for publication in Classical and Quantum Gravity Subj-class: General Relativity and Quantum Cosmology: Other: Fluid Dynamics
- 02.40.Ma
- 04.70.-s
- 04.20.Gz
- 04.20.Cv
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