Global Structure of Evaporating Black Holes
  By extending the charged Vaidya metric to cover all of spacetime, we obtain a Penrose diagram for the formation and evaporation of a charged black hole. In this construction, the singularity is time-like. The entire spacetime can be predicted from initial conditions if boundary conditions at the singularity are known. 
Maulik K. Parikh and Frank Wilczek