VACUUM FLUCTUATION FORCE ON A RIGID CASIMIR CAVITY IN DE SITTER AND SCHWARZSCHILD–DE SITTER SPACE–TIME

Abstract

We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases: de Sitter space–time, de Sitter space–time with weak gravitational field and Schwarzschild–de Sitter space–time. In de Sitter space–time the resulting net force follows the square inverse law but unfortunately it is too weak to be measurable due to the large universe radius. By introducing a weak gravitational field into the de Sitter space–time, we find that the net force can now be split into two parts, one is the gravitational force due to the induced effective mass between the two plates and the other one is generated by the metric structure of de Sitter space–time. In order to investigate the vacuum fluctuation force on the rigid cavity under strong gravitational field, we perform a similar analysis in Schwarzschild–de Sitter space–time and results are obtained in three different limits. The most interesting one is when the cavity gets closer to the horizon of a blackhole, square inverse law is recovered and the repulsive force due to negative energy/mass of the cavity now has an observable strength. More importantly the force changes from being repulsive to attractive when the cavity crosses the event horizon, so that the energy/mass of the cavity switches the sign, which suggests the unusual time direction inside the event horizon.