Thick domain walls around a black hole
  We discuss the gravitationally interacting system of a thick domain wall and a black hole. We numerically solve the scalar field equation in the Schwarzschild spacetime and obtain a sequence of static axi-symmetric solutions representing thick domain walls. We find that, for the walls near the horizon, the Nambu--Goto approximation is no longer valid. 
Yoshiyuki Morisawa, Daisuke Ida, Akihiro Ishibashi, and Ken-ichi Nakao