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

Abstract

In this study we show that, from arbitrarily dispersed initial data, both the focusing of electromagnetic fields and the concentration of gravitational waves could lead to the formation of trapped surfaces. We establish a scale–critical semi–global existence result from past null infinity for the Einstein–Maxwell system by assigning the signature for decay rates to both geometric quantities and Maxwell components. This result generalizes an approach of the first author in [4] on studying the Einstein vacuum equations to the physical Einstein-Maxwell system by employing additional elliptic estimates and geometric renormalizations and it also extends a result of Yu [18] and serves as the first scale-critical result for Einstein's equations coupled with matter.