Analogue models of gravity at eleven parameters
Abstract
Analogue models of gravity realise the wave equation of a massless field on a curved metric in a flowing medium. In condensates they have measured the Hawking radiation of a sonic horizon. They have measured the quanta produced by expanding and bouncing universes, and the ringdown of a rotating geometry. This letter asks what they can do for the theory at eleven parameters, whose gravity is Einstein's in vacuum. Three transpositions are exact. The body horizon of the theory is the event horizon thickened by the probing body's Compton wavelength. In a condensate it is the sonic horizon thickened by √ 2 times the healing length, at the temperature of the chemical potential over 2π. The torsion bounce of the theory is a ramp of the scattering length, (1 + t 2 /t 2 b ) -2/3 . The quanta it produces have the spectrum computed here, 0.16/(kt b ) 2 in the infrared and a thermal tail. The quantised circulation of a giant vortex is the Kerr radius of a body of spin N ℏ, N Compton lengths. What no analogue reaches is the dynamics, the identities of the theory and the bounce density. A spinor condensate, whose spin density enters the acoustic metric quadratically, is the one platform where the contact term has a counterpart.
Related
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BibTeX
@misc{reynaud2026analogue,
title = {{Analogue models of gravity at eleven parameters}},
author = {Patrick B. Reynaud},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05798277v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analogue models of gravity at eleven parameters
AU - Patrick B. Reynaud
PY - 2026
DA - 2026/10/13
PB - HAL
UR - https://hal.science/hal-05798277v1
AB - Analogue models of gravity realise the wave equation of a massless field on a curved metric in a flowing medium. In condensates they have measured the Hawking radiation of a sonic horizon. They have measured the quanta produced by expanding and bouncing universes, and the ringdown of a rotating geometry. This letter asks what they can do for the theory at eleven parameters, whose gravity is Einstein's in vacuum. Three transpositions are exact. The body horizon of the theory is the event horizon thickened by the probing body's Compton wavelength. In a condensate it is the sonic horizon thickened by √ 2 times the healing length, at the temperature of the chemical potential over 2π. The torsion bounce of the theory is a ramp of the scattering length, (1 + t 2 /t 2 b ) -2/3 . The quanta it produces have the spectrum computed here, 0.16/(kt b ) 2 in the infrared and a thermal tail. The quantised circulation of a giant vortex is the Kerr radius of a body of spin N ℏ, N Compton lengths. What no analogue reaches is the dynamics, the identities of the theory and the bounce density. A spinor condensate, whose spin density enters the acoustic metric quadratically, is the one platform where the contact term has a counterpart.
ER -