Boundary effects on the thermal stability of a black hole at the centre of a conducting spherical shell

This paper reports calculations and analysis of the effects of a perfect conducting wall of a very large spherical shell on the stable thermodynamic equilibrium of a black hole sitting at the centre of the shell which is filled with Electromagnetic blackbody radiation. A parallel is drawn with the case where electromagnetic is replaced by scalar blackbody radiation with Dirichlet or Neumann boundary conditions on the wall. It is found that the value of the shell radius above which only blackbody radiation remains in stable thermodynamic equilibrium can be considerably affected by vacuum polarization due to the presence of the wall.