Analogue Gravity
Carlos Barceló · Stefano Liberati · Matt Visser
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In one page
Carlos Barceló, Stefano Liberati and Matt Visser survey an entire research programme: building working models of curved spacetime out of ordinary matter. Their cleanest example is sound in a moving fluid. Push the flow past the speed of sound and sound waves inside that region can never fight their way back upstream — you have made an acoustic horizon, what the field calls a dumb hole. The authors show this is far more than a metaphor. Linearise the fluid equations and the sound field obeys exactly the wave equation of a massless scalar field on a curved metric, an acoustic metric assembled from the fluid’s density, its flow velocity and its speed of sound. From there they catalogue analogues in Bose-Einstein condensates, superfluid helium, slow light, optical fibres and water tanks, and report the first laboratory measurements of the predicted effects. Their closing argument is the one that matters most here: spacetime geometry may be emergent, the long-wavelength limit of a medium, exactly as fluid mechanics is the long-wavelength limit of molecules.
Why it matters hereThis is the standard reference for chapter 5’s central move — treating the vacuum as a medium whose excitations see an effective metric — and it supplies chapter 4 with the point that a metric can be engineered by shaping a flow rather than by assembling a mass.
What it claims
01Acoustics 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, ‘The Simplest Example of an Analogue Spacetime’; Eq. 24 and following
Settled physics02Where the flow speed exceeds the speed of sound, the sound cones tip past the vertical and an acoustic horizon forms — a region sound cannot escape — and the surface gravity of that horizon can be computed directly from the flow, so the analogy carries the whole causal structure of a black hole, not just its name.Sections 2.2–2.7; surface-gravity calculation, Eqs. 65–68
Settled physics03The analogy extends all the way to the quantum level: a horizon in a moving medium is predicted to emit phononic Hawking radiation, which makes curved-space quantum field theory a laboratory subject rather than an astrophysical one.Section 1, Introduction; Section 5.1
Published and peer-reviewed04Laboratory work has already measured pieces of the effect — mode conversion and negative-frequency waves in the Nice wave tank, stimulated Hawking emission in the Vancouver wave tank whose Bogoliubov coefficients satisfy the expected Boltzmann relation, and a sonic horizon created in a Bose-Einstein condensate.Section 6, ‘Experimental efforts’; Sections 6.1–6.2; Eq. 310
Published and peer-reviewed05Gravity itself may not be fundamental. Just as density and velocity make no sense at the molecular level and emerge only on averaging, the spacetime manifold and its metric may emerge only once one averages over microphysical degrees of freedom — Sakharov’s induced gravity read through condensed matter.Section 7.7, ‘Emergent gravity’
What to watch06The open problem is dynamics, not kinematics: no known condensed-matter system satisfies the conditions — in particular Lorentz-scale dominance over the bosonisation scale — that would make the induced dynamics Einstein’s equations, and in helium-3 the induced dynamics comes out fluid-mechanical instead. Finding a medium that meets those conditions is the measurement to watch.Section 7.8, ‘One specific route to the Einstein equations?’
What to watch
The way in
https://link.springer.com/article/10.12942/lrr-2011-3Open access in Living Reviews in Relativity under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Germany licence, which permits sharing but not derivative works, so this page carries a summary rather than the text. The same review, in the identical May 2011 revision, is free to read as arXiv gr-qc/0505065v3.
How to cite it
Carlos Barceló, Stefano Liberati, Matt Visser (2011) Analogue Gravity. doi:10.12942/lrr-2011-3
Where it sits in the curriculum
The vacuum as a quantum fluidThe metric, warp drives and wormholesThe evidence ladder