Black Hole evaporation in semi-classical approach
  As well as known, the black hole evaporation problem is famous problem. Because the S.W.Hawking found the black holes emit light at the future null infinity as a thermal radiation \cite{H}, we think that the black holes may be vanish. However, to prove this problem, we should solve field equation, i.e. forth order partial differential equations \cite{Ford}\cite{BD}. However, we can find a method to solve this equation, and we could prove that the black holes finally vanish. To solve this problem we use dynamical horizons equation in the Vaidya spacetime. 
Shintaro Sawayama
physics.gen-ph