Scalar absorption beyond geometric optics in Klein-Gordon-separable Johannsen black hole spacetimes

Johannsen metric is a natural and significant generalization of the Kerr metric, representing the most general stationary, axisymmetric spacetime that preserves the Carter constant of motion. The theoretical status furnishes a powerful, systematic framework for strong-field tests of the no-hair theorem and for investigations of deviations from Kerr black-hole geometries. We formulate massless scalar plane-wave absorption in a Klein-Gordon-separable subclass of Johannsen spacetimes. In the asymptotically flat Johannsen metric, we impose Klein-Gordon separability, derive the separated angular and radial equations, and build a partial wave framework for the leading deformation sectors $A_1(r)$, $A_2(r)$, and $A_5(r)$. The resulting description separates deformations that change the radial size function $X(r)$ from those that enter only the radial kinetic term. The former modify the low-frequency area law, the high-frequency null-capture cross section, and the finite-frequency absorption spectra, whereas a pure $A_5$ deformation leaves the leading null-capture observable unchanged while remaining detectable in wave propagation. We further examine off-axis incidence, co-/counter-rotating contributions, and superradiant modes, where changes in $X(r_+)$ shift the horizon angular velocity and hence the superradiant threshold. Our results identify finite-frequency absorption as a wave-optics diagnostic that can probe radial propagation sectors inaccessible to both the area law and null geodesic capture observables, offering a new tool for strong-field tests of black hole geometry.