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

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Abstract
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 spherical cavity. The values of radial pressure, tangential pressure and energy density depend on the coordinate radius of the cavity. For large cavities the author recovers the results of Candelas (1980), obtaining a negative energy density near the horizon. As the cavity radius decreases, the energy density first decreases to a minimum and then increases through zero to positive values.