Causal structure of acoustic spacetimes

TL;DR

This paper explores the causal structure of acoustic spacetimes in fluid systems, highlighting similarities and differences with general relativity, especially around sonic horizons, to understand how effective metrics model causal relations without Einstein's equations.

Contribution

It provides a detailed analysis of the causal structure in acoustic spacetimes, emphasizing the role of sonic points and horizons, and compares these with standard relativistic causal structures.

Findings

Acoustic spacetimes can exhibit horizons similar to black holes.

Causal structures in acoustic models differ from general relativity near sonic points.

Effective metrics in fluids can mimic relativistic causal features.

Abstract

The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved spacetime. Specifically, the propagation of acoustic disturbances in moving fluids are described by ``effective metrics'' that carry with them notions of ``causal structure'' as determined by an exchange of sound signals. These acoustic causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. (After all, the underlying fluid mechanics is governed by the equations of traditional hydrodynamics, not by the Einstein equations.) In this article we take a careful look at what can be said about the causal structure of acoustic spacetimes, focusing on those containing sonic points or horizons, both with a view to seeing what is different from standard general relativity, and to seeing what the similarities might be.