Hydrodynamic models of astrophysical wormholes. The general concept

We study hydrodynamic models of astrophysical wormholes when water waves can be amplified in the course of propagation between two critical points where wave and current speeds coincide. Such models can be realised in shallow laboratory ducts with variable width and depths. In this paper, we derive the basic set of equations for shallow water waves on the spatially variable flow in the duct of a variable cross-section and present the asymptotic analysis of solutions in the neighbourhood of the critical points. The critical points mimic either the black hole (BH) horizon if the flow transits from the subcritical to the supercritical regime, or the white hole (WH) horizon if the flow transits from the supercritical to the subcritical regime. We study then, the wave propagation in the flow with two horizons when the flow transits first the BH horizon and then the WH one. The region between the horizons mimics a wormhole in general relativity. For the sake of completeness, we also study the successive transition through WH and BH horizons. The theoretical results are illustrated by numerical calculations of wave propagation in both these arrangements. It is shown that the wave amplification after passing the active zone between the horizons takes place in BH{WH arrangements only and can occur for different relationships between the subcritical and supercritical flow velocities. The frequency dependence of the amplification factor is obtained and quantified in terms of the velocity ratio within and outside the \wormhole domain". In the next paper, we plan to present exact solutions for the specific velocity profile.
Comment: 49 pages, 18 figures, 2 tables