Casimir energy for spherical shell in Schwarzchild black hole background

In this paper, we consider the Casimir energy of massless scalar field which satisfy Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.Comment: 10 pages, no figure,discussion added, references added, has been accepted for the publication in GR

Finite-temperature scalar fields and the cosmological constant in an Einstein universe

We study the back reaction effect of massless minimally coupled scalar field at finite temperatures in the background of Einstein universe. Substituting for the vacuum expectation value of the components of the energy-momentum tensor on the RHS of the Einstein equation, we deduce a relationship between the radius of the universe and its temperature. This relationship exhibit a maximum temperature, below the Planck scale, at which the system changes its behaviour drastically. The results are compared with the case of a conformally coupled field. An investigation into the values of the cosmological constant exhibit a remarkable difference between the conformally coupled case and the minimally coupled one.Comment: 7 pages, 2 figure