On the thin wall limit of thick planar domain walls
  Considering a planar gravitating thick domain wall of the $\lambda \phi^4$ theory, we demonstrate how the Darmois junction conditions written on the boundaries of the thick wall with the embedding spacetimes reproduce the Israel junction condition across the wall when one takes its thin wall limit. 
S. Ghassemi, S. Khakshournia, and R. Mansouri