We prove that any complete Riemannian manifold with negative part of the Ricci curvature in a suitable Dynkin class is bi-Lipschitz equivalent to a finite-dimensional \({{\,\textrm{RCD}\,}}\) space, by building upon the transformation rule of the Bakry–Émery condition under time change. We apply this result to show that our previous results on the limits of closed Riemannian manifolds satisfying a uniform Kato bound (Carron et al. in Limits of manifolds with a Kato bound on the Ricci curvature. II. arXiv:2205.01956, 2022; Catino et al. in Geom Funct Anal 34(1):1–18, 2024) carry over to limits of complete manifolds. We also obtain a weak version of the Bishop–Gromov monotonicity formula for manifolds satisfying a strong Kato bound.
