Mathematics – Analysis of PDEs
Scientific paper
2011-05-30
Mathematics
Analysis of PDEs
2 figures, 66 pages
Scientific paper
The purpose of the paper is to understand a mechanism of evolutionary formation of trapped surfaces when there is an electromagnetic field coupled to the background space-time. Based on the short pulse ansatz, on a given finite outgoing null hypersurface which is free of trapped surfaces, we exhibit an open set of initial data for Einstein equations coupled with a Maxwell field, so that a trapped surface forms along the Einstein-Maxwell flow. On one hand, this generalizes the black-hole-formation results of Christodoulou and Klainerman-Rodnianski. In fact, by switching off the electromagnetic field in our main theorem, we can retrieve their results in vacuum. On the other hand, this shows that the formation of black hole can be purely due to the condensation of Maxwell field on the initial null hypersurface where there is no incoming gravitational energy.
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