Reconsidering the black hole final state in Dirac fields

We extend Horowitz and Maldacena's proposal about black hole final state to Dirac fields and find that if annihilation of the infalling positrons and the collapsed electrons inside the horizon is considered, then the nonlinear evolution of collapsing quantum state will be avoided. We further propose that annihilation also plays the central role in the process of black hole information escaping in both Dirac and scalar fields. The computation speed of a black hole is briefly discussed in the end.