Phonon tunnels across a sonic horizon
  We consider phonon tunneling in sonic black hole by WKB approximation method without the backreaction, in which the relativistic momentum-energy equation is used. We also study the WKB loop (closed path) integral [B. D. Chowdhury, Pramana70:3-26, 2008] in sonic black hole case and discuss the equivalence of the results of some cases from the two different tunneling probability expression in Painlev\'e-like coordinates. 
H. Z. Fang and K. H. Zhou
gr-qc