Acoustic black holes: horizons, ergospheres, and Hawking radiation

TL;DR

This paper explores how acoustic disturbances in flowing fluids can be modeled using Lorentzian geometry, creating an analogy with black hole physics, including horizons and Hawking radiation.

Contribution

It establishes a detailed analogy between fluid flow phenomena and black hole physics using Lorentzian geometry, defining horizons and ergospheres in acoustic systems.

Findings

Defined acoustic horizons and ergospheres in fluid flows

Established the analogy between acoustic metrics and black hole metrics

Proposed using fluid models to study Hawking radiation

Abstract

It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. This question can be answered by invoking the language of Lorentzian differential geometry: If the fluid is barotropic and inviscid, and the flow is irrotational (though possibly time dependent), then the equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3+1)-dimensional Lorentzian geometry. The acoustic metric governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound. This rather simple physical system is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows. Many results and definitions can be carried over directly from one system to another. For example, I will show how to define the ergosphere, trapped regions, acoustic apparent horizon, and acoustic event horizon for a supersonic fluid flow, and will exhibit the close relationship between the acoustic metric for the fluid flow surrounding a point sink and the Painleve-Gullstrand form of the Schwarzschild metric for a black hole. This analysis can be used either to provide a concrete non-relativistic model for black hole physics, up to and including Hawking radiation, or to provide a framework for attacking acoustics problems with the full power of Lorentzian differential geometry.