Statistical Entropy and Superradiance in 2+1 Dimensional Acoustic Black   Holes
  We study ``draining bathtub'' as an acoustic analogue of a three-dimensional rotating black hole. Rotating fluid near the sonic horizon necessarily gives rise to the superradiant modes, which are partially responsible for the thermodynamic quantities in this rotating vortex-like hole. Using the recently suggested thin-layer method overcoming some difficulties from the well-known brick-wall method, we explicitly calculate the free energy of the system by treating the superradiance carefully and obtain the desirable entropy formula. 
Wontae Kim, Young-Jai Park, Edwin J. Son, Myung Seok Yoon