Conserved Energy Flux for the Spherically Symmetric System and the Backreaction Problem in the Black Hole Evaporation

For the spherically symmetric system, we prove the existence o{ a new locally cotEen·ecl flux which can be interpreted to represent the total energy flux of matter and gravitational field. ·with the aid of this conservation law, we study the relation between the behavior of the event horizon and the energy flux across it and look for constraints imposed on the total energy radiated to infinity. Some implications of the results of this study to the backreaction problem in the black hole evaporation are discussed.