Acoustic analogues of black hole singularities

TL;DR

This paper explores how certain fluid dynamics systems can serve as analogues to black hole singularities, providing insights into gravitational phenomena through fluid models.

Contribution

It demonstrates an exact mapping between the equations of black hole systems with sources and the steady motion of fluids with planar sources, highlighting differences in singularity concepts.

Findings

Fluid systems can model black hole sources without divergences.

Exact mathematical correspondence between gravitational and fluid dynamics equations.

Discussion on the different interpretations of singularities in fluids and gravity.

Abstract

We search for acoustic analogues of a spherical symmetric black hole with a pointlike source. We show that the gravitational system has a dynamical counterpart in the constrained, steady motion of a fluid with a planar source. The equations governing the dynamics of the gravitational system can be exactly mapped in those governing the motion of the fluid. The different meaning that singularities and sources have in fluid dynamics and in general relativity is also discussed. Whereas in the latter a pointlike source is always associated with a (curvature) singularity in the former the presence of sources does not necessarily imply divergences of the fields.