R-layer Mode Theory LXXXIV-B: Rotational Deformations, Kerr Information Geometry, and Multi-band Observables

This Volume LXXXIV-B extends the R-layer Mode Theory (RLMT) to rotating black holes by incorporating Kerr geometry, frame dragging, and spin-dependent information dynamics. We introduce a dimensionless Kerr parametrization of the R-layer effective geometry and quantify how frame dragging modifies the information stress tensor and the coupling of tensor perturbations. The CUP core, previously symmetric in the non-rotating case, acquires a spin-induced deformation that feeds back into the Fisher information kernel and the near-horizon dynamics. We derive spin- and m-dependent corrections to the effective radial potential for tensor perturbations, extending the Teukolsky formalism with R-layer-induced mass and dissipation kernels. These corrections lead to shifts in the Kerr quasi-normal mode spectrum and the scrambling rate. We also construct a parameterization of R-layer-induced deviations in the Kerr shadow radius and echo amplitudes, and extend the Fisher information analysis to the parameter space (M, a*, AR). This Volume provides a unified information-geometric description of rotating black holes within RLMT and yields concrete multi-band observational predictions for ringdown signals, horizon-scale imaging, and echo searches. It forms the rotating counterpart to Volume LXXXIV-A and completes the foundation for future comparisons with gravitational-wave and black-hole imaging data.