Black holes: interfacing the classical and the quantum

Abstract

The central idea advocated in this paper is that {forming the black hole horizon is attended with transition from the classical regime of evolution to the quantum one}. We justify the following criterion for discriminating between the classical and the quantum: {spontaneous creations and annihilations of particle-antiparticle pairs are impossible in the classical world but possible in the quantum world}. We show that it is sufficient to {change the overall sign of the spacetime signature in the classical picture of field propagation for it to be treated as its associated quantum picture}. To describe a self-gravitating object at the last stage of its classical evolution, we propose to use the Foldy--Wouthuysen representation of the Dirac equation in curved spacetimes, and the Gozzi classical path integral. In both approaches, maintaining the dynamics in the classical regime is controlled by supersymmetry.

comment: LaTeX, 12 pages