A simple flux criterion for trapped surface formation by short pulses of gravitational radiation and matter

We discuss the formation of trapped surfaces induced by short pulses of incoming gravitational radiation and matter fields, in a double-null formulation. We identify a hierarchy of orders in the pulse width for the geometric and matter quantities consistent with the evolution equations. Under the assumption that this hierarchy holds throughout the region considered, the incoming fluxes undergo approximately conservative inward transport and are thereby amplified. The Raychaudhuri equation then gives an initial flux criterion for trapped surface formation. The conditions on the matter are expressed through the Ricci components and their derivatives, which allows the argument to be developed without specifying a particular matter model.