Demonstration of the spike phenomenon using the LTB models

TL;DR

This paper demonstrates how permanent spikes can form in LTB models, providing a potential mechanism for large cosmic structures, with numerical examples showing direct formation in matter density.

Contribution

It introduces the occurrence of permanent spikes in LTB models and shows they can form directly in matter density, expanding understanding of structure formation in general relativity.

Findings

Permanent spikes occur in LTB models.

Spikes can form directly in matter density.

Numerical examples illustrate spike formation.

Abstract

We demonstrate the occurrence of permanent spikes using the Lemaitre-Tolman-Bondi models, chosen because the solutions are exact and can be analyzed by qualitative dynamical systems methods. Three examples are given and illustrated numerically. The third example demonstrates that spikes can form directly in the matter density, as opposed to indirectly in previous studies of spikes in the Kasner regime. Spikes provide an alternative general relativistic mechanism for generating exceptionally large structures observed in the Universe.