Quantum black holes as classical space factories

TL;DR

This paper explores how classical space and matter may emerge from fundamental quantum dynamics, using a geometric approach inspired by elasticity theory and quantum field methods, particularly in the context of black-hole evaporation.

Contribution

It introduces a novel method applying boson transformation to quantum gravity, deriving curvature, torsion, and matter fields from quantum origins, advancing the understanding of emergent classical spacetime.

Findings

Curvature and torsion emerge naturally from quantum models.

Disclinations relate to spin structures and matter fields.

Non-Abelian contributions to geometric tensors are derived from elasticity theory.

Abstract

Space and matter may both be manifestations of a single fundamental quantum dynamics, as it may become evident during black-hole evaporation. Inspired by the fact that quantum electrodynamics underlies the classical theory of elasticity, that in turn has a natural and well-known geometric description in terms of curvature and torsion, related to topological defects, here we move some necessary steps to find the map from such fundamental quantum level to the emergent level of classical space and quantum matter. We proceed by adapting the boson transformation method of standard quantum field theory to the quantum gravity fundamental scenario and successfully obtain the emergence of curvature and torsion, our main focus here. In doing so, we have been able to overcome difficult issues of interpretation, related to the Goldstone modes for rotational symmetry. In fact, we have been able to apply the boson transformation method to disclinations, to relate them to the spin structure and to give an heuristic derivation of the matter field equation on curved space. We also improve results of previous work on the emergence of geometric tensors from elasticity theory, as the non-Abelian contributions to the torsion and curvature tensors, postulated in those papers, here emerge naturally. More work is necessary to identify the type of gravity theories one can obtain in this way.