A Note on trapped Surfaces in the Vaidya Solution
  The Vaidya solution describes the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole. There has been a question whether closed trapped surfaces can extend into the flat region (whereas closed outer trapped surfaces certainly can). For the special case of self-similar collapse we show that the answer is yes, if and only if the mass function rises fast enough. 
Ingemar Bengtsson, Jos\'e M. M. Senovilla