Blow-Up of Test Fields Near Cauchy Horizons

TL;DR

This paper demonstrates that solutions to nonlinear wave equations near a Cauchy horizon in certain spacetimes develop singularities, preventing smooth extension beyond the horizon, using energy methods.

Contribution

It establishes generic blow-up results for test fields near Cauchy horizons in Taub and Moncrief spacetimes, extending understanding of horizon stability.

Findings

Solutions cannot be smoothly extended through the Cauchy horizon.

Blow-up occurs for generic initial data in these spacetimes.

Results apply to various matter models.

Abstract

The behaviour of test fields near a compact Cauchy horizon is investigated. It is shown that solutions of nonlinear wave equations on Taub spacetime with generic initial data cannot be continued smoothly to both extensions of the spacetime through the Cauchy horizon. This is proved using an energy method. Similar results are obtained for the spacetimes of Moncrief containing a compact Cauchy horizon and for more general matter models.