Electromagnetic Casimir Effect in AdS Spacetime

Abstract

We investigate the vacuum expectation value (VEV) of the energy-momentum tensor for the electromagnetic field in anti-de Sitter (AdS) spacetime in the presence of a boundary parallel to the AdS horizon. On the boundary, the field obeys the generalized perfect conductor boundary condition. The VEV of the energy-momentum tensor is decomposed into the boundary-free and boundary-induced contributions. In this way, for points away from the boundary, the renormalization is reduced to that for AdS spacetime without the boundary. The boundary-induced energy density is negative everywhere, and the normal stress is positive in the region between the boundary and the AdS boundary and is negative in the region between the boundary and the AdS horizon. Near both the AdS boundary and horizon, the boundary-induced VEV decays exponentially as a function of the corresponding proper distance. Applications are given for even and odd vector fields in Randall–Sundrum model with a single brane.

Keywords

• Casimir effect
• anti-de Sitter space
• electromagnetic field