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We address the issues of the scattering of massless planar scalar waves by anacoustic black hole in neo-Newtonian hydrodynamics. We then compute thedifferential cross section through the use of the partial wave approach in theneo-Newtonian theory which is a modification of the usual Newtonian theory thatcorrectly incorporates the effects of pressure. We mainly show that thescattering of planar waves leads to a modified analogue Aharonov-Bohm effectdue to a nontrivial response of the parameters defining the equation of state.

Analogue Aharonov-Bohm effect in neo-Newtonian theory