HIGH-TEMPERATURE EXPANSION OF STRING FREE-ENERGY HYPERBOLIC SPACE

The high temperature behavior of the open bosonic string free energy i n the space S-1 circle times H-N with vanishingly small curvature is i nvestigated. The leading term of the high temperature expansion of the one-loop free energy, near the Hagedorn instability, is obtained. The problem of ir regularization of thermodynamical quantities is pointed out. For minimally coupling quantum fields related to the normal mode s of strings, the results are similar to the ones valid for Rindler sp ace. In the lower mass string states regime a connection with the quan tum corrections to the black hole entropy is outlined.