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

TL;DR

This paper investigates how a conducting spherical shell influences the thermal stability of a central black hole surrounded by electromagnetic or scalar radiation, highlighting the impact of boundary conditions and vacuum polarization.

Contribution

It provides a detailed analysis of boundary effects on black hole thermodynamics within a spherical shell, including the influence of vacuum polarization on stability thresholds.

Findings

Shell radius affects stable equilibrium conditions.

Vacuum polarization significantly alters stability thresholds.

Electromagnetic and scalar cases show similar boundary effects.

Abstract

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.