Vortex geometry for the equatorial slice of the Kerr black hole
Abstract
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.
Cite
@article{arxiv.gr-qc/0409014,
title = {Vortex geometry for the equatorial slice of the Kerr black hole},
author = {Matt Visser and Silke Weinfurtner},
journal= {arXiv preprint arXiv:gr-qc/0409014},
year = {2009}
}
Comments
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