A scale-critical trapped surface formation criterion for the Einstein-Maxwell system

In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the formation of trapped surfaces. We establish a scale-critical semi-global existence result from the past null infinity for the Einstein-Maxwell system by assigning the signature for decay rates to geometric quantities and Maxwell components. This result generalizes an approach of the first author on studying Einstein vacuum equations by employing additional elliptic estimates and geometric renormalizations, and it also extends a result of Yu to the scale-critical regime.