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

TL;DR

This paper explores how quasiparticles in certain fluid flows experience an effective curved spacetime geometry described by the Painleve-Gullstrand metric, using concepts from general relativity to analyze their propagation.

Contribution

It applies general relativity tools to characterize the effective spacetime geometry experienced by quasiparticles in specific hydrodynamic flows, highlighting curvature effects.

Findings

Quasiparticle trajectories follow null geodesics in the effective geometry.

The effective geometry exhibits Riemannian curvature in various flow scenarios.

Analysis of flows like shear, vortex, and rotation reveals curvature influences on quasiparticle behavior.

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.