Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 37C / c / i / Solution

Outside the ingoing null shell the enclosed mass is $E$, so use the ingoing Ingoing Eddington-Finkelstein coordinatesThis is the Schwarzschild metric of mass $E$, regular across $r=2E$ and valid for $r>0$ on the exterior side of the shell.