Black Holes: Interfacing the Classical and the Quantum

The central idea of this paper is that forming the black hole horizon is attended with the transition from the classical regime of evolution to the quantum one. We offer and justify the following criterion for discriminating between the classical and the quantum: creations and annihilations of particle-antiparticle pairs are impossible in the classical reality but possible in the quantum reality. In flat spacetime, we can switch from the classical picture of field propagation to the quantum picture by changing the overall sign of the spacetime signature. To describe a self-gravitating object at the final 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.