Quantum effects in acoustic black holes: The backreaction

We investigate the backreaction equations for an acoustic black hole formed in a Laval nozzle under the assumption that the motion of the fluid is one-dimensional. The solution in the near-horizon region shows that as phonons are (thermally) radiated the sonic horizon shrinks and the temperature decreases. This contrasts with the behavior of Schwarzschild black holes, and is similar to what happens in the evaporation of (near-extremal) Reissner-Nordström black holes (i.e., infinite evaporation time). Finally, by appropriate boundary conditions the solution is extended in both the asymptotic regions of the nozzle.

Figure 1

A Laval nozzle. The waist of the nozzle represents the sonic horizon ($|\overrightarrow{v}|=c$). In the region on the right of the waist $|\overrightarrow{v}|<c$ and on the left $|\overrightarrow{v}|>c$ (sonic hole).