Vacuum polarization on black hole space times

The effects of vacuum polarization in black hole space times are examined. Particular attention is given to the vacuum physics inside the event horizon. The analytic properties of the solutions to the radial wave equation in Schwarzs child space time as functions of argument, frequency, and angular momentum are given. These functions are employed to define the Feynmann Green function (G/sub F/(x,x') for a scalar field subject to the Hartle-Hawking boundary conditions. An examination of the Schwarzschild mode functions near r = 0 is provided. This work is necessary background for a future calculation of and the quantum stress-energy tensor for small r. Some opinions are given on how this calculation might be performed. A solution of the one-loop Einstein equations for Schwarzs child Anti-deSitter (SAdS) space time is presented, using Page's approximation to the quantum stress tensor. The resulting perturbed metric is shown to be unphysical, as it leads to a system of fields with infinite total energy. This problem is believed to be due to a failure of Page's method in SAdS. Suggestions are given on how one might correct the method