On the effective acoustic geometry for relativistic viscous fluids

TL;DR

This paper uses the Hadamard-Papapetrou method to derive an effective acoustic geometry for relativistic viscous fluids, enabling the study of acoustic black holes in dissipative fluid models.

Contribution

It introduces a novel approach to describe acoustic perturbations in viscous fluids via an effective metric, extending previous models to include dissipative effects.

Findings

Effective metric for viscous fluids derived

Acoustic black hole models in viscous fluids analyzed

Dissipative effects incorporated into acoustic geometry

Abstract

Hadamard-Papapetrou method of field discontinuities is here employed in order to determine the effective metric that describes the propagation of acoustic perturbations in isentropic fluids. It is shown that, when dissipative effects are present, small perturbations in fastly moving fluids have a natural description in terms of an effective acoustic geometry. As an application of our results, a model for an acoustic black hole in viscous fluid is investigated.