Thick Domain Walls and Charged Dilaton Black Holes
  We study a black hole domain wall system in dilaton gravity which is the low-energy limit of the superstring theory. We solve numerically equations of motion for real self-interacting scalar field and justify the existence of static axisymmetric field configuration representing the thick domain wall in the background of a charged dilaton black hole. It was also confirmed that the extreme dilaton black hole always expelled the domain wall. 
R. Moderski, M. Rogatko