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On the space-time curvature experienced by quasiparticle excitations in the Painleve-Gullstrand effective geometry

Uwe R. Fischer·Matt Visser
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Abstract

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.

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Uwe R. Fischer, Matt Visser. 2003-02-03. On the space-time curvature experienced by quasiparticle excitations in the Painleve-Gullstrand effective geometry. https://doi.org/10.1016/s0003-4916(03)00011-3

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