Acoustic analogs of two-dimensional black holes

TL;DR

This paper introduces a method to create acoustic analogs of 2D black holes, linking fluid dynamics with black hole thermodynamics, and applies it to specific cases like the Schwarzschild black hole.

Contribution

It provides a general framework for modeling 2D and 4D black holes as acoustic analogs using fluid dynamics, establishing thermodynamic properties from fluid equations.

Findings

Acoustic analogs replicate black hole thermodynamics.

Fluid dynamics equations encode black hole mass, temperature, and entropy.

Application to Schwarzschild and Anti-de Sitter black holes.

Abstract

We present a general method for constructing acoustic analogs of the black hole solutions of two-dimensional (2D) dilaton gravity. Because by dimensional reduction every spherically symmetric, four-dimensional (4D) black hole admits a 2D description, the method can be also used to construct analogue models of 4D black holes. We also show that after fixing the gauge degrees of freedom the 2D gravitational dynamics is equivalent to an one-dimensional fluid dynamics. This enables us to find a natural definition of mass $M$, temperature $T$ and entropy $S$ of the acoustic black hole. In particular the first principle of thermodynamics $dM=TdS$ becomes a consequence of the fluid dynamics equations. We also discuss the general solutions of the fluid dynamics and two particular cases, the 2D Anti-de sitter black hole and the 4D Schwarzschild black hole.