FINITE-TEMPERATURE EFFECTS FOR MASSIVE FIELDS IN D-DIMENSIONAL RINDLER-LIKE SPACES

The first quantum corrections to the free energy for massive fields in D-dimensional space-times of the form R x R(+) x M(N-1), where D = N + 1 and M(N-1) is a constant curvature manifold, is investigated by me ans of the zeta-function regularization. It is suggested that the natu re of the divergences, which are present in the thermodynamical quanti ties, might be better understood making use of the conformal related o ptical metric and associated techniques. The general form of the horiz on divergences of the free energy is obtained as a function of the fre e energy densities of fields having negative square masses (absence of the gap in the Laplace operator spectrum) on ultrastatic manifolds wi th hyperbolic spatial section H-N-2n and of the Seeley-DeWitt coeffici ents of the Laplace operator on the manifold M(N-1). Furthermore, recu rrence relations are found relating higher and lower dimensions. The c ases of Rindler space, where M(N-1) = R(N-1) and very massive D-dimens ional black holes, where M(N-1) = S-N-1, treated as examples. The reno rmalization of the internal energy is also discussed.