Casimir effect in background of static domain wall

In this paper we investigate the vacuum expectation values of energy-moment um tenser for conformally coupled scalar field in the standard parallel pla te geometry with Dirichlet boundary conditions and in the background of pla nar domain wall case. First we calculate the vacuum expectation values of e nergy-momentum tenser by using the mode sums, then we show that correspondi ng properties can be obtained by using the conformal properties of the prob lem. The vacuum expectation values of energy-momentum tenser contain two te rms which come from the boundary conditions and the the gravitational backg round. In the Minkowskian limit our results agree with those obtained in Re f. 3.