Generating spiky solutions of Einstein field equations with the Stephani transformation

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 the Stephani transformation with the rotational Killing vector field of the locally rotationally symmetric Jacobs solution. The late-time permanent spike occurs along the cylindrical axis. 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.

arXiv commentPhD thesis. arXiv admin note: text overlap with arXiv:gr-qc/0410126 by other authors

References in corpus (19)

• Quiescent cosmological singularities
• Numerical Investigation of Cosmological Singularities
• Numerical Approaches to Spacetime Singularities
• Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
• Asymptotic Behavior of the $T^3\times R$ Gowdy Spacetimes
• Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on $T^3\times R$
• Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometry
• Spikes in the Mixmaster regime of G_2 cosmologies
• A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation
• Spike Oscillations
• New explicit spike solution -- non-local component of the generalized Mixmaster attractor
• High velocity spikes in Gowdy spacetimes
• Numerical Relativity and Inhomogeneous Cosmologies
• Generating matter inhomogeneities in general relativity
• Spikes and matter inhomogeneities in massless scalar field models
• An exact smooth Gowdy-symmetric generalized Taub-NUT solution
• General relativistic density perturbations
• What is General Relativity?
• Stiff fluid spike solutions from Bianchi type V seed solutions

Cited by in corpus (3)

• Cylindrical spikes
• Numerical confirmations of joint spike transitions in $G_2$ cosmologies
• Transition analysis of the non-OT $G_2$ stiff fluid spike solution