Hawking Radiation from a Vaidya Black Hole: A Semi-Classical Approach   and Beyond
  We derive the Hawking radiation for Vaidya black hole in the tunneling picture from the corresponding single particle action by the use of the radial null geodesic and the Hamilton-Jacobi method (beyond semi-classical approximation). Both results are then analyzed and compared. 
Haryanto M. Siahaan and Triyanta