Topological effects in the polarization of the Fulling-Rindler vacuum

Abstract

We investigate how the compactification of some spatial dimensions in Rindler spacetime affects the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a charged scalar field prepared in the Fulling-Rindler vacuum state. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. For a general number of spatial dimensions, the components of the VEVs are explicitly separated, corresponding to the expectation values in the Minkowski vacuum. As a limiting case, the VEVs are retrieved in Rindler spacetime with trivial topology. We demonstrate that, for non-zero phases in the periodicity conditions, the vacuum energy-momentum tensor exhibits off-diagonal components with indices in the compact subspace. Near the Rindler horizon, the leading terms in the asymptotic expansions of the field squared and the diagonal components of the energy-momentum tensor coincide with the corresponding VEVs in Rindler spacetime with trivial topology. The off-diagonal components of the energy-momentum tensor vanish on the Rindler horizon. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. The exception to this is a massless field with zero phases in the periodicity conditions. In this special case, the difference decays according to a power law as a function of acceleration. As an application, we consider the VEVs near the horizon of cylindrical black holes and topological black holes with toroidal horizons.