Polarisation of the vacuum near a black hole inside a spherical cavity

The renormalised expectation value in the Hartle-Hawking vacuum of the stress-energy tensor of a massless conformally coupled scalar field is discussed near the horizon of a Schwarzschild black hole inside a spheric cavity. The values of radial pressure, tangential pressure and energy density depend on the coordinate radius of the cavity. For large cavities the results of Candelas (Phy. Rev.; D21: 2185 (1980)) are recovered, that is a negative energy density is obtained near the horizon. As the cavity radius decreases, the energy density first decreases to a minimum and then increases through zero to positive values. (author)