Shell Perturbation Theory from the FCLET Action

We develop the perturbation-theoretic strong-field sector of the finite-capacity latency–erasure theory by deriving the shell reflectivity problem directly from the FCLET action. Earlier FCLET work established the local burden variables, fixed the shell-onset condition , derived the shell location, and obtained the echo-delay scale of saturation-shell compact objects. What remained open was the decisive strong-field problem: once a finite-capacity shell forms, how do perturbations propagate across it, what matching law does the shell impose, and how does the reflectivity function arise from the action itself? This paper answers that question. We construct the strong-field FCLET action in a static spherically symmetric shell background, linearize the coupled metric-latency system, and derive the shell perturbation problem in covariant form. In the odd-parity sector, the scalar latency perturbation does not propagate as an independent axial degree of freedom, but it dresses the background shell structure and modifies the effective Regge–Wheeler problem through shell-localized coupling. In the strict thin-shell limit, this yields a shell-supported axial master equation with a localized interaction term, from which the first explicit FCLET shell reflectivity law is derived analytically. We obtain together with the corresponding transmission coefficient and shell response scale. The minimal axial thin-shell branch is therefore fully reflective in magnitude in the deep infrared, transparent in the ultraviolet, and governed by the crossover scale . This result establishes the first action-derived reflectivity sector of the FCLET compact-object program. The paper also shows why the minimal branch is not the final physical shell-response sector of the theory. A realistic FCLET reflectivity law requires finite-thickness shell dynamics, coupled metric-latency perturbations, and dissipative internal shell channels. The present result is therefore both decisive and delimitative: it proves that is derivable from the perturbation problem rather than inserted phenomenologically, and it identifies exactly what must be added to obtain the fully physical shell-response law. The strong-field FCLET program thus advances from shell kinematics to shell perturbation dynamics. The shell is no longer characterized only by where it forms and when its echoes return. It is now characterized by a derived boundary-response sector.