The Acoustic Analogue of the Reissner-Nordstr\"om Metric

Some analogues in solid state physics allow us to gain a better understanding of certain aspects of gravity. A canonical acoustic metric of a Bose-Einstein condensate based on the Schwarzschild metric has been developed [M.~Visser, ``Acoustic black holes: Horizons, ergospheres, and Hawking radiation,'' Class.\ Quant.\ Grav.\ {\bf 15}, 1767 (1998) [gr-qc/9712010]]. We extend that approach to the Reissner-Nordstr\"om metric. To do this, we start by looking at a test charge in a plasma described by a Bose-Einstein condensate scalar field. The resulting potential, a modified Yukawa potential, is then used to determine an acoustic analogue of the Reissner-Nordstr\"om metric. We anticipate that this approach will yield a testable description of the analogue model.