On the first $G_1$ stiff fluid spike solution in General Relativity

TL;DR

This paper presents the first exact stiff fluid spike solution in General Relativity with a single isometry, providing insights into spike crossings and structure formation.

Contribution

It introduces a novel exact solution to Einstein's equations exhibiting a spacelike G_1 symmetry and a persistent spike crossing, advancing understanding of spike phenomena.

Findings

First exact stiff fluid spike solution with G_1 symmetry

Solution exhibits a persistent spike crossing

Enhances understanding of spike crossings in structure formation

Abstract

Using the Geroch transformation we obtain the first example of an exact stiff fluid spike solution to the Einstein field equations in a closed form exhibiting a spacelike $G_1$ group of symmetries (i.e., with a single isometry). This new solution is of Petrov type I and exhibits a spike crossing which persists to the past, which allows us to better understand spike crossings in the context of structure formation.