Spike Oscillations

TL;DR

This paper explores the complex behavior of spacelike singularities, focusing on oscillations and spike formations, and demonstrates how these phenomena can be understood through concatenations of exact solutions in a normalized state space, revealing potential hidden symmetries.

Contribution

It introduces a unified description of BKL and spike oscillations using exact solutions in a Hubble-normalized framework, expanding the understanding of singularity dynamics.

Findings

Spike oscillations involve inhomogeneous vacuum models.

Sequences of exact solutions explain oscillatory behavior.

Results suggest hidden symmetries in singularity evolution.

Abstract

According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatial point evolves independently from its neighbors, in an oscillatory manner that is represented by a sequence of Bianchi type I and II vacuum models. Recent investigations support a modified conjecture: The formation of spatial structures (`spikes') breaks asymptotic locality. The complete description of a generic spacelike singularity involves spike oscillations, which are described by sequences of Bianchi type I and certain inhomogeneous vacuum models. In this paper we describe how BKL and spike oscillations arise from concatenations of exact solutions in a Hubble-normalized state space setting, suggesting the existence of hidden symmetries and showing that the results of BKL are part of a greater picture.