Non-orthogonally transitive $G_2$ spike solution

TL;DR

This paper extends the known orthogonally transitive $G_2$ spike solution to a more general non-OT case using Geroch's transformation, resulting in a solution that always resolves its spike and has additional parameters.

Contribution

It introduces a new non-OT $G_2$ spike solution with extra parameters, expanding the understanding of spike behavior in cosmological models.

Findings

The new solution always resolves its spike.

It contains two additional parameters compared to the OT $G_2$ solution.

The solution is obtained via Geroch's transformation on a Kasner seed.

Abstract

We generalize the orthogonally transitive (OT) $G_2$ spike solution to the non-OT $G_2$ case. This is achieved by applying Geroch's transformation on a Kasner seed. The new solution contains two more parameters than the OT $G_2$ spike solution. Unlike the OT $G_2$ spike solution, the new solution always resolves its spike.