vacuum stress between conducting plates for neumann’s condition

In [1], we have found that the curved spacetime version of the vacuum stress between conducting plates was first done in flat spacetime by brown and maclay. here, we calculate the energy-momentum tensor for the casimir effect of parallel plates under neumann boundary conditions to support our recent results found in [2]. we use direct calculation of energy-momentum tensor by employing the well understood point splitting method of regularization, and we show that the there is first order correction to the casimir energy in curved spacetime proportional to gm/c2r where r and m are the radius and the mass of the source of gravity.