Black holes: interfacing the classical and the quantum

TL;DR

This paper explores the transition from classical to quantum regimes in black hole formation, proposing criteria based on particle-antiparticle pair creation and using advanced mathematical frameworks to describe the quantum aspects of black holes.

Contribution

It introduces a novel criterion for distinguishing classical and quantum regimes in black hole formation and applies the Foldy–Wouthuysen transformation and Gozzi path integral to model quantum effects.

Findings

Changing spacetime signature links classical and quantum descriptions.

Supersymmetry controls the classical regime dynamics.

Proposes new methods to describe quantum black hole states.

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.