Cylindrical spikes

TL;DR

This paper introduces a new method to generate solutions with late-time permanent spikes in spacetime models, revealing complex transient behaviors and leading to a revised understanding of spike phenomena.

Contribution

The authors develop a novel application of the Geroch/Stephani transformation to produce late-time permanent spikes and analyze transient structures with a new technique, expanding spike theory.

Findings

Discovery of late-time permanent spikes along the cylindrical axis

Identification of a new transient behavior called the overshoot transition

Revised understanding of transient spike phenomena

Abstract

The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a solution with a late-time permanent spike. We achieve this by applying Stephani's transformation with the rotational Killing vector field of the locally rotationally symmetric Jacobs solution. The late-time permanent spike occurs along the cylindrical axis. Using a mixed Killing vector field, the generated solution also features a rich variety of transient structures. We introduce a new technique to analyse these structures. Our findings lead us to discover a transient behaviour, which we call the overshoot transition. These discoveries compel us to revise the description of transient spikes.