Experimental Black-Hole Evaporation?
William G. Unruh
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In one page
Hawking’s 1974 result — that a black hole glows with a thermal spectrum — was beautiful and, it seemed, untestable. In three pages William Unruh showed that you do not need a black hole. Write down the ordinary equations for a fluid flowing without friction, linearise them for small sound waves, and what comes out is exactly the equation for a massless field moving in a curved spacetime, with the speed of sound playing the part of the speed of light. Where the flow speeds up past the speed of sound, that geometry has a horizon: sound made beyond it can never swim back out. Unruh then quantises the sound field and gets Hawking’s answer again — the sonic horizon should give off a thermal hiss of phonons, at a temperature set by how sharply the flow accelerates through the crossing. He estimates a few ten-millionths of a degree above absolute zero for a millimetre-wide throat, and notes that this is a far easier experiment than making a small black hole.
Why it matters hereThis is the paper that turned the vacuum’s deepest predictions into laboratory work. Chapter 5’s picture of the vacuum as a fluid is not a metaphor here — it is an exact correspondence, and it is why chapter 3 can treat horizon physics as something you build rather than something you wait for. Chapter 13 needs precisely this bridge: one set of equations describing sound in water, light in a moving medium and fields near a black hole, all at once.
What it claims
01Take the standard equations of an irrotational fluid — Euler, continuity, and a pressure that depends only on density — and linearise them about any background flow. The equation that governs small disturbances of the velocity potential is exactly the equation for a massless scalar field propagating in a curved geometry, with a metric built from the background density, the background flow velocity and the local sound speed. This is a mathematical identity, not an analogy.Page 1351, the linearised equations, through the acoustic metric displayed at the head of page 1352
Settled physics02If the background flow is steady and converging, and somewhere crosses the local speed of sound smoothly, then near that crossing the acoustic metric takes the same form the Schwarzschild metric takes near a black-hole horizon. Unruh writes both metrics side by side to make the correspondence explicit. That surface is a sonic horizon: sound generated inside it cannot climb back out against the flow.Page 1352, the transonic expansion of the radial velocity and the comparison with the Schwarzschild line element
Settled physics03Quantise the sound field and the correspondence carries the physics with it. An observer drifting through the sonic horizon with the fluid sees the phonon field in its ordinary vacuum state, and the modes therefore behave, in the co-moving time, exactly as a scalar field does near a Schwarzschild horizon for a freely falling observer. The consequence is that the sonic black hole emits sound with a thermal spectrum, filtered by a greybody factor, at a temperature equal to Planck’s constant over two pi times Boltzmann’s constant, multiplied by the rate at which the flow velocity changes across the horizon.Page 1352 into 1353, the mode expansion and the displayed temperature formula
Settled physics04The result does not lean on the idealisations used to derive it. Unruh states in his notes that the conclusions depend only on the existence of a sonic horizon, not on the assumed spherical symmetry or on the particular smooth transonic profile, and that a model of transonic flow through a shaped nozzle gives exactly the same result.Page 1353, notes 5 and 8
Settled physics05The system is offered as a working laboratory for the parts of black-hole evaporation nobody can otherwise reach. The fluid equations are known to fail at atomic distances, just as a smooth spacetime is expected to fail at the Planck scale, so the sonic model lets you ask what a short-distance breakdown does to the emission. And the emitted phonons are themselves fluctuations of the flow, so they alter their own propagation in exactly the way graviton emission alters the spacetime that carries it.Page 1353, the paragraph beginning with the theoretical-laboratory argument
What to watch06Unruh gives the number and the honest difficulty in the same breath. Taking the velocity gradient at the horizon as the sound speed divided by the horizon radius, the predicted temperature is roughly three ten-millionths of a kelvin for a sound speed of 300 metres per second and a horizon one millimetre across — low enough that turbulence in a small nozzle would likely swamp it, but, in his words, a much simpler experimental task than creating a tiny black hole.Page 1353, the numerical temperature estimate and the closing paragraph
Designed, not yet built
The way in
https://doi.org/10.1103/PhysRevLett.46.1351WHAT THIS PAGE IS WRITTEN FROM. Physical Review Letters volume 46, number 21, pages 1351 to 1353, published 25 May 1981, received 8 December 1980, by W. G. Unruh of the Department of Physics, University of British Columbia, Vancouver. The article is closed access under the APS default licence; the version of record was read in full for this sheet on 2026-09-08 through the APS harvest service, and no text of it is reproduced here. Every locator below cites a page and passage of that three-page Letter. The registry carried the author as W. G. Unruh; the given-name form William G. Unruh is used here. The work was supported in part by an Alfred P. Sloan Foundation fellowship and by the Natural Sciences and Engineering Research Council of Canada, with facilities provided by the Center for Theoretical Physics at the University of Texas at Austin.
How to cite it
William G. Unruh (1981) Experimental Black-Hole Evaporation?. doi:10.1103/PhysRevLett.46.1351
Where it sits in the curriculum
What the vacuum isInertia and gravity from the vacuumThe unified pictureThe vacuum as a quantum fluid