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Spin fluctuations enter the calculation of the superconducting transitiontemperature T$_c$ only in the next-to-leading order (i.e., in O(1/N$^2$) of the1/N expansion of the t-J model. We have calculated these terms and show thatthey have only little influence on the value of T$_c$ obtained in the leadingorder O(1/N) in the optimal and overdoped region, i.e., for dopings larger thanthe instability towards a flux phase. This result disagrees with recentspin-fluctuation mediated pairing theories. The discrepancies can be tracedback to the fact that in our case the coupling between electrons and spins isdetermined by the t-J model and not adjusted and that the spin susceptibilityis rather broad and structureless and not strongly peaked at low energies as inspin-fluctuation models. Relating T$_c$ and transport we show that theeffective interactions in the particle-particle and particle-hole channels arenot simply related within the 1/N expansion by different Fermi surface averagesof the same interactin as in the case of phonons or spin fluctuations. As aresult, we find that large values for T$_c$ and rather small scattering ratesin the normal state as found in the experiments can easily be reconciled witheach other. We also show that correlation effects heavily suppress transportrelaxation rates relative to quasiparticle relaxation rates in the case ofphonons but not in the case of spin fluctuations.Comment: 16 pages, 10 figures, will appear in Phys. Rev.

Influence of spin fluctuations on the superconducting transition temperature and resistivity in thet-Jmodel at largeN