R-layer Mode Theory (RLMT) LXXXI: Quantum Information Stress Tensor, Black Hole Physics, and Multi-band Observables

This volume initiates Phase III of R-layer Mode Theory (RLMT), where quantum information plays a central role in gravitational and cosmological dynamics. We construct the quantum information stress tensor from the Fisher information kernel and the second variation of the modular Hamiltonian, define the R-layer generalized entropy, and formulate the R-layer quantum extremal surface (QES). A holographic correspondence between boundary modular flow and R-layer modular flow is established. We apply this framework to black hole spacetimes, deriving R-layer corrections to the Regge–Wheeler and Teukolsky equations, and compute shifts in quasi-normal mode spectra and scrambling rates. Finally, we obtain multi-band observational predictions for CMB-S4, LISA, and PTA, and provide numerical implementations of the Fisher kernel and R-layer corrected QNM spectrum. This volume demonstrates how RLMT unifies quantum information, black hole physics, and gravitational-wave phenomenology within a single operator-theoretic structure.