# Dynamical structures specific to strong gravitational field: Quantum formalism

## TL;DR

This paper introduces a quantum formalism using affine quantization to analyze special structures called wiggles in Bianchi IX spacetime near singularities, aiming to understand their quantum behavior and implications for the BKL scenario.

## Contribution

It develops a novel affine quantization approach to study the quantum fate of classical wiggles in Bianchi IX spacetime, linking classical and quantum structures.

## Key findings

- Classical wiggles are characterized and their properties are analyzed.
- A formalism for comparing classical and quantum wiggles is proposed.
- Potential insights into quantum aspects of the BKL scenario are discussed.

## Abstract

The dynamics of the general Bianchi IX spacetime, near the gravitational singularity, underlies the Belinskii, Khalatnikov and Lifshitz scenario. Asymptotically, near the singularity, the oscillations of the directional scale factors (defining the spacetime metric) are freezed so the evolution of the Bianchi IX model is devoid of chaotic features. However, it includes special structures, that we call the wiggles, which change their properties in the asymptotic regime. We propose the formalism, based on an affine quantization scheme, to examine the fate of the wiggles at the quantum level. We present the way of comparing the classical wiggles with their quantum counterparts. We expect that our work may contribute towards understanding some quantum aspects of the BKL scenario.