Manufacture of Gowdy spacetimes with spikes

Abstract

In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.

25 pages

References in corpus (1)

• Analytic description of singularities in Gowdy spacetimes

Cited by in corpus (46)

• Numerical Approaches to Spacetime Singularities
• The past attractor in inhomogeneous cosmology
• Numerical simulations of generic singuarities
• Theorems on existence and global dynamics for the Einstein equations
• Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometry
• Asymptotic expansions close to the singularity in Gowdy spacetimes
• Spikes in the Mixmaster regime of G_2 cosmologies
• A Hamiltonian Formulation of the BKL Conjecture
• Dynamical systems approach to G2 cosmology
• Asymptotic isotropization in inhomogeneous cosmology
• The loop quantum cosmology bounce as a Kasner transition
• Spike Oscillations
• New explicit spike solution -- non-local component of the generalized Mixmaster attractor
• Numerical relativity with the conformal field equations
• Second-order hyperbolic Fuchsian systems and applications
• Fuchsian analysis of S^2xS^1 and S^3 Gowdy spacetimes
• Recent developments concerning generic spacelike singularities
• High velocity spikes in Gowdy spacetimes
• Cosmological models from a dynamical systems perspective
• Gowdy phenomenology in scale-invariant variables
• Cauchy horizons in Gowdy space times
• Spikes and matter inhomogeneities in massless scalar field models
• Fuchsian methods and spacetime singularities
• An exact smooth Gowdy-symmetric generalized Taub-NUT solution
• Spacetime Singularities: Recent Developments
• Is general relativity `essentially understood' ?
• Do spikes persist in a quantum treatment of spacetime singularities?
• Second-order hyperbolic Fuchsian systems. Asymptotic behavior of geodesics in Gowdy spacetimes
• Computing Gowdy spacetimes via spectral evolution in future and past directions
• A New Class of Asymptotically Non-Chaotic Vacuum Singularities
• Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant
• On the relation between mathematical and numerical relativity
• Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Stiff fluid spike solutions from Bianchi type V seed solutions
• The fine structure of Gowdy spacetimes
• On the first $G_1$ stiff fluid spike solution in General Relativity
• Localized big bang stability for the Einstein-scalar field equations
• On the initial geometry of a vacuum cosmological spacetime
• Generating Gowdy cosmological models
• Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0\le K<1/3$
• Dynamics of solutions of the Einstein equations with twisted Gowdy symmetry
• Non-orthogonally transitive $G_2$ spike solution
• Demonstration of the spike phenomenon using the LTB models
• Electrocardiogram of the Mixmaster Universe
• Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces
• The electromagnetic spike solutions