Microscopic Picture of Non-Relativistic Classicalons

TL;DR

This paper explores a non-relativistic scalar field model as a prototype for classicalizing theories like gravity, analyzing quantum fluctuations and supporting the idea of black holes as Bose-Einstein condensates of gravitons.

Contribution

It introduces a toy model mimicking black hole physics, investigates quantum fluctuations, and provides evidence supporting black holes as graviton condensates.

Findings

Quantum fluctuations invalidate perturbative approaches due to high mode occupation.

The model supports the view of black holes as Bose-Einstein condensates of gravitons.

Indicates the need for non-linear numerical analysis of the model.

Abstract

A theory of a non-relativistic, complex scalar field with derivatively coupled interaction terms is investigated. This toy model is considered as a prototype of a classicalizing theory and in particular of general relativity, for which the black hole constitutes a prominent example of a classicalon. Accordingly, the theory allows for a non-trivial solution of the stationary Gross-Pitaevskii equation corresponding to a black hole in the case of GR. Quantum fluctuations on this classical background are investigated within the Bogoliubov approximation. It turns out that the perturbative approach is invalidated by a high occupation of the Bogoliubov modes. Recently, it was proposed that a black hole is a Bose-Einstein condensate of gravitons that dynamically ensures to stay at the verge of a quantum phase transition. Our result is understood as an indication for that claim. Furthermore, it motivates a non-linear numerical analysis of the model.