Vacuum Polarisation and the Black Hole Singularity

In order to investigate the effects of vacuum polarisation on mass inflation singularities, we study a simple toy model of a charged black hole with cross flowing radial null dust which is homogeneous in the black hole interior. In the region $r^2 \ll e^2$ we find an approximate analytic solution to the classical field equations. The renormalized stress-energy tensor is evaluated on this background and we find the vacuum polarisation backreaction corrections to the mass function $m(r)$. Asymptotic analysis of the semiclassical mass function shows that the mass inflation singularity is much stronger in the presence of vacuum polarisation than in the classical case.