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The purpose of the paper is to understand a mechanism of evolutionaryformation of trapped surfaces when there is an electromagnetic field coupled tothe background space-time. Based on the short pulse ansatz, on a given finiteoutgoing null hypersurface which is free of trapped surfaces, we exhibit anopen 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 ofChristodoulou and Klainerman-Rodnianski. In fact, by switching off theelectromagnetic field in our main theorem, we can retrieve their results invacuum. On the other hand, this shows that the formation of black hole can bepurely due to the condensation of Maxwell field on the initial nullhypersurface where there is no incoming gravitational energy.

Dynamical formation of black holes due to the condensation of matter field