Reissner-Nordstrom Black Holes and Thick Domain Walls
  We solve numerically equations of motion for real self-interacting scalar fields in the background of Reissner-Nordstrom black hole and obtained a sequence of static axisymmetric solutions representing thick domain walls charged black hole systems. In the case of extremal Reissner-Nordstrom black hole solution we find that there is a parameter depending on the black hole mass and the width of the domain wall which constitutes the upper limit for the expulsion to occur. 
R. Moderski, M. Rogatko