Acoustic horizons in nuclear fluids

TL;DR

This paper investigates how weak dispersion affects acoustic horizons in nuclear fluid flows, revealing that even minimal dispersion destabilizes static horizons and renders them opaque to incoming disturbances.

Contribution

It introduces a nonlinear hydrodynamic model for nuclear fluids, analyzing the impact of weak dispersion on acoustic horizons and demonstrating their destabilization and opacity.

Findings

Weak dispersion destabilizes static acoustic horizons.

Horizons become fully opaque to incoming disturbances.

Amplitude and energy flux of perturbations decay exponentially outside the horizon.

Abstract

We consider a hydrodynamic description of the spherically symmetric outward flow of nuclear matter, accommodating dispersion in it as a very weak effect. About the resulting stationary conditions in the flow, we apply an Eulerian scheme to derive a fully nonlinear equation of a time-dependent radial perturbation. In its linearized limit, with no dispersion, this equation implies the static acoustic horizon of an analogue gravity model. We, however, show that time-dependent nonlinear effects destabilize the static horizon. We also model the perturbation as a high-frequency travelling wave, and perform a {\it WKB} analysis, in which the effect of weak dispersion is studied iteratively. We show that even arbitrarily small values of dispersion make the horizon fully opaque to any acoustic disturbance propagating against the bulk flow, with the amplitude and the energy flux of the radial perturbation undergoing a discontinuity at the horizon, and decaying exponentially just outside it.