On emerging scarred surfaces for the Einstein vacuum equations

TL;DR

This paper extends previous work on Einstein vacuum equations by proving an optimal semi-global existence result and demonstrating the formation of complex scarred surfaces with multiple pre-scarred components.

Contribution

It introduces an improved semi-global existence theorem and shows the formation of multi-component pre-scarred surfaces in Einstein vacuum spacetimes.

Findings

Extended semi-global existence to an optimal range.

Proved formation of surfaces with multiple pre-scarred components.

Enhanced understanding of trapped surface formation in general relativity.

Abstract

This is a follow up on our previous work in which we have presented a modified, simpler version of the remarkable recent result of Christodoulou on the formation of trapped surfaces. In this paper we prove two related results. First we extend the semi-global existence result, which was at the heart of our previous work, to an optimal range. We then use it to establish the formation of surfaces with multiple pre-scarred angular components.