Dust thin shell limit of a thick wall

Abstract

We consider the vanishing thickness limit of a wall separating Minkowski spacetime from Schwarzschild or Friedmann spacetime with the purpose of obtaining the thin shell described by the Israel matching formalism. We show that the thin shell cannot be a limit of the wall consisting of Lemaitre-Tolman-Bondi dust. To successfully implement the required limit, it is necessary to add anisotropy to the stress tensor of the wall matter. For such anisotropic matter, we derive boundary conditions that allow carrying out the limit. Finally, we provide an example of a solution satisfying these conditions.