Non-stationary Black Hole and Hawking Radiation in 1+1 Dimensions

A non-stationary solution of the field equation in 1+1 dimension gravity is given with the advanced Eddington-Finkelstein coordinate. There exists a 1 +1 dimensional non-stationary black hole in the space-time. The location of event horizons, the Hawking temperature and the spectrum of thermal radiation are derived.