Historical research guide · 0052 · 2011
Analogue Gravity
Carlos Barceló · Stefano Liberati · Matt Visser
In one minute
In this 2011 review, Barceló, Liberati and Visser explain how waves in materials can follow equations resembling those for fields in curved spacetime. A sufficiently fast fluid flow can prevent sound from travelling upstream, creating an acoustic counterpart of a black-hole horizon. The review compares water waves, ultracold atomic condensates and optical systems, examining where each analogy applies. It reports classical stimulated Hawking emission in water-wave experiments and a sonic horizon in a condensate kept stable for about eight milliseconds. At that time, reproducible detection of spontaneous quantum Hawking radiation remained an experimental target. The authors distinguish this effective geometry for waves from the equations governing gravity itself: reproducing curved-spacetime propagation does not automatically reproduce Einstein’s gravitational dynamics.
Connection
A flowing fluid can change the paths available to sound waves. The same equations that describe those waves also describe fields on a curved metric, giving experiments a way to test horizon physics and explore how geometry can emerge from a material.
From the source
Acoustics in a moving fluid is a genuine analogue spacetime: linearising the Euler and continuity equations for a barotropic, inviscid, irrotational flow gives, exactly, the wave equation of a massless scalar field propagating on an acoustic metric built from the background density, the speed of sound and the flow velocity.Section 2.3, Physical acoustics; theorem and equations 6–7, 24–34
In a steady inward flow, a trapping horizon occurs where the inward component of the flow, perpendicular to the horizon, reaches the local speed of sound. A supersonic region alone is an ergoregion and need not form a horizon; the review treats the two separately and derives acoustic surface gravity from the flow.Sections 2.4.1, Horizons and ergo-regions, and 2.4.2, Surface gravity; equations 43–44 and 65–78
In suitable quantum analogue systems, horizon formation is predicted to produce Hawking radiation carried by phonons or other field excitations. The review examines how the medium’s dispersion, the preparation of the flow and background temperature affect this prediction and its detection.Section 5.1.1, Basics, especially requirements 1–2 and issues 1–5
The 2011 review describes negative-frequency mode conversion in the Nice wave tank, classical stimulated Hawking emission in the Vancouver experiment with the expected Boltzmann relation between mode coefficients, and a sonic horizon maintained for about eight milliseconds in a Bose–Einstein condensate.Sections 6.1–6.2, Wave tank experiments and Bose–Einstein condensate experiments; equation 310
The authors explore whether spacetime and its metric could emerge from microscopic degrees of freedom, much as fluid density and bulk velocity describe collective molecular behaviour. Analogue systems provide examples of emergent geometry for waves; the further question is how gravitational dynamics could emerge too.Section 7.7, Emergent gravity; section 7.8, One specific route to the Einstein equations?
For the route to Einstein’s equations discussed in the 2011 review, relativistic behaviour must persist well above the bosonisation energy scale, and induced dynamics must dominate any existing contribution. The authors report that helium-3 and other systems then known did not meet these conditions; helium-3 instead gives fluid-mechanical dynamics.Section 7.8, One specific route to the Einstein equations?, conditions 1–3 and following discussion
The way in
https://link.springer.com/article/10.12942/lrr-2011-3How to cite it
Carlos Barceló, Stefano Liberati, Matt Visser (2011) Analogue Gravity doi:10.12942/lrr-2011-3