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This paper reports calculations and analysis of the effects of a perfectconducting wall of a very large spherical shell on the stable thermodynamicequilibrium of a black hole sitting at the centre of the shell which is filledwith Electromagnetic blackbody radiation. A parallel is drawn with the casewhere electromagnetic is replaced by scalar blackbody radiation with Dirichletor Neumann boundary conditions on the wall. It is found that the value of theshell radius above which only blackbody radiation remains in stablethermodynamic equilibrium can be considerably affected by vacuum polarizationdue to the presence of the wall.

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