On emerging scarred surfaces for the Einstein vacuum equations

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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.