Finite temperature contributions to the renormalized energy-momentum tensor for an arbitrary curved space-time

The finite temperature contributions to the effective Lagrangian and energy-momentum tensor in the cases of scalar and spinor fields are evaluated by means of the Green's function method. The results are obtained in an arbitrary curved space-time by adiabatic expansions of the Green's functions.We would like to thank professor D. Ivanenko for support of our work and many stimulating discussions.