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

Abstract

Inthisstudyweshowthat, fromarbitrarilydispersedinitialdata, boththefocusingofelectromagnetic 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 geometric quantities and Maxwell components. This result generalizes an approach of the first author on studying the Einstein vacuum equations by employing additional elliptic estimates and geometric renormalizations and it also extends a result of Yu to the scale–critical regime.