What Did We Learn from Studying Acoustic Black Holes ? the Motivation for the Analogy

The study of acoustic black holes has been undertaken to provide new insights about the role of high frequencies in black hole evaporation. Because of the infinite gravitational redshift from the event horizon, Hawk-ing quanta emerge from configurations which possessed ultra high (trans-Planckian) frequencies. Therefore Hawking radiation cannot be derived within the framework of a low energy effective theory; and in all derivations there are some assumptions concerning Planck scale physics. The analogy with condensed matter physics was thus introduced to see if the asymptotic properties of the Hawking phonons emitted by an acoustic black hole, namely stationarity and thermality, are sensitive to the high frequency physics which stems from the granular character of matter and which is governed by a non-linear dispersion relation. In 1995 Unruh showed that they are not sensitive in this respect, in spite of the fact that phonon propagation near the (acoustic) horizon drastically differs from that of photons. In 2000 the same analogy was used to establish the ro-bustness of the spectrum of primordial density fluctuations in inflationary models. This analogy is currently stimulating research for experimenting Hawking radiation. Finally it could also be a useful guide for going beyond the semi-classical description of black hole evaporation. The semi-classical description of black hole evaporation is based on the hypothesis that the dynamics of the system (black hole + radiation) can be well approximated by treating the gravitational field classically. In this case the quantized radiation field φ obeys the d'Alembert equation 1 √ −g ∂ µ √ −gg µν ∂ ν φ = 0 , (1) where g µν is the metric of the collapsing body. Following Hawking[1], one obtains that an isolated black hole formed by gravitational collapse radiates