High velocity spikes in Gowdy spacetimes

TL;DR

This paper investigates the evolution of high-velocity spikes in Gowdy spacetimes, revealing how initial spike velocities influence their persistence or disappearance over time.

Contribution

It provides a detailed classification of spike behavior based on initial velocities, extending understanding of spike dynamics in Gowdy spacetimes.

Findings

High initial velocity spikes tend to be driven to lower velocities.

Spikes with certain initial velocity ranges persist with specific final velocities.

Other spikes with different initial velocities eventually disappear.

Abstract

We study the behavior of spiky features in Gowdy spacetimes. Spikes with velocity initially high are, generally, driven to low velocity. Let n be any integer greater than or equal to 1. If the initial velocity of an upward pointing spike is between 4n-3 and 4n-1 the spike persists with final velocity between 1 and 2, while if the initial velocity is between 4n-1 and 4n+1, the spiky feature eventually disappears. For downward pointing spikes the analogous rule is that spikes with initial velocity between 4n-4 and 4n-2 persist with final velocity between 0 and 1, while spikes with initial velocity between 4n-2 and 4n eventually disappear.