Spikes and matter inhomogeneities in massless scalar field models

TL;DR

This paper explores the formation and properties of spikes in massless scalar field models within general relativity, introducing new solutions and analyzing how matter influences spike dynamics.

Contribution

It presents new exact and generalized spike solutions for stiff fluid models, including non-OT G_2 solutions, and discusses their qualitative behavior and implications for scalar field physics.

Findings

New exact OT G_2 stiff fluid spike solution

Generalization of vacuum spike solutions to stiff fluid case

Matter influences spike formation and can lead to permanent spikes

Abstract

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) $G_2$ stiff fluid spike models both heuristically and numerically, and give a new exact OT $G_2$ stiff fluid spike solution. We then present a new two-parameter family of non-OT $G_2$ stiff fluid spike solutions, obtained by the generalization of non-OT $G_2$ vacuum spike solutions to the stiff fluid case by applying Geroch's transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions, in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT $G_2$ stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes.