The Casimir effect of Reissner--Nordström black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a ( 1+1)-dimensional Reissner--Nordstr?m black hole background is calculated by using Wald's axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.