Relativistic Acoustic Geometry

TL;DR

This paper explores how sound waves behave in a relativistic fluid, showing they can be described by a curved spacetime geometry similar to general relativity, and introduces new concepts like the acoustic horizon and surface gravity.

Contribution

It develops a relativistic acoustic geometry framework, deriving the acoustic metric tensor and analog surface gravity in curved spacetime for the first time.

Findings

Sound wave propagation is equivalent to a massless scalar field in curved spacetime.

Relativistic supersonic flows can have ergospheres and acoustic horizons analogous to black holes.

A general-relativistic expression for acoustic surface gravity is derived.

Abstract

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved space-time geometry. The geometry is described by the acoustic metric tensor that depends locally on the equation of state and the four-velocity of the fluid. For a relativistic supersonic flow in curved space-time the ergosphere and acoustic horizon may be defined in a way analogous the non-relativistic case. A general-relativistic expression for the acoustic analog of surface gravity has been found.