Hydrodynamic models of astrophysical wormholes: the general concept

We study the amplification of shallow-water waves in the course of their propagation in a duct of a variable cross section with a spatially inhomogeneous flow. We derive the basic set of equations for the wave propagation and present the asymptotic analysis of solutions in the neighborhood of critical points where the wave speed coincides with the speed of the current. The considered model represents a kinematic analog of astrophysical event horizons occurring in the vicinity of the black holes (BH) or white holes (WH). We study then the wave propagation in the flow with two critical points (two horizons) when the flow transits first the BH horizon and then the WH one or vice versa. In the former case, the region between the critical points mimics a wormhole in general relativity. The theoretical results are illustrated by numerical calculations of wave propagation through the critical points. 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'