Tidal deformation bounds and perturbation transfer in bounded curvature spacetimes

We derive two model-independent results for spacetimes with globally bounded tidal fields. These are operational resolution scales of the local-inertial approximation and tidal dynamics; no spacetime discreteness is implied. Given an invariant bound $$\lambda _{\max }\le \lambda _\textrm{bound}$$ λ max ≤ λ bound on the electric Riemann eigenvalues $$E_{ij}\equiv R_{\hat{0}i\hat{0}j}$$ E ij ≡ R 0 ^ i 0 ^ j along freely falling worldlines, we prove (i) a rigorous upper bound on accumulated geodesic deviation through any bounded curvature interior, controlled by $$\tau _*\equiv \lambda _{\max }^{-1/2}$$ τ ∗ ≡ λ max - 1 / 2 , and (ii) the existence of a critical wavenumber $$k_*\sim \tau _*^{-1}$$ k ∗ ∼ τ ∗ - 1 separating adiabatic from non-adiabatic perturbation transfer through high-curvature epochs, with Bogoliubov coefficients exponentially suppressed for $$k\,\tau _*\gg 1$$ k τ ∗ ≫ 1 . Both results depend only on the tidal bound (and, for mode transfer, on a mild timescale assumption for the curvature-driven effective potential) and are otherwise insensitive to metric details. For preparation, we collect the standard operational consequences of bounded curvature, including the accuracy-dependent local-inertial domain $$L_\textrm{LI}(\varepsilon )\sim \sqrt{\varepsilon }\, \lambda _{\max }^{-1/2}$$ L LI ( ε ) ∼ ε λ max - 1 / 2 and, for conformally flat cores in four dimensions, the benchmark ratio $$\tau _*/L_*=24^{1/4}$$ τ ∗ / L ∗ = 24 1 / 4 with $$L_*\equiv K_{\max }^{-1/4}$$ L ∗ ≡ K max - 1 / 4 . We quantify the robustness of this coefficient under departures from maximal symmetry via the Weyl-to-Kretschmann ratio $$\epsilon _C$$ ϵ C . The general framework is validated numerically in the extremal Hayward geometry.