2002/05/31 by Uwe R. Fischer, Matt Visser · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #cond-mat #gr-qc
paper · pdf · doi:10.1016/s0003-4916(03)00011-3
published as Annals Phys. 304 (2003) 22-39 · 9 RevTex4 pages, 1 figure, minor modifications, to appear in Annals of Physics (N.Y.)
arxiv created 2003/02/03 · openalex publication_date 2003/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider quasiparticle propagation in constant-speed-of-sound (iso-tachic) and almost incompressible (iso-pycnal) hydrodynamic flows, using the technical machinery of general relativity to investigate the ``effective space-time geometry'' that is probed by the quasiparticles. This effective geometry, described for the quasiparticles of condensed matter systems by the Painleve-Gullstrand metric, generally exhibits curvature (in the sense of Riemann), and many features of quasiparticle propagation can be re-phrased in terms of null geodesics, Killing vectors, and Jacobi fields. As particular examples of hydrodynamic flow we consider shear flow, a constant-circulation vortex, flow past an impenetrable cylinder, and rigid rotation.