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Gravitational Spectra and Wave Propagation in Regular Black Holes Supported by a Dehnen Halo

We investigate gravitational perturbations, quasinormal modes, grey-body factors, and absorption cross-sections of the recently proposed regular and asymptotically flat black hole supported by a Dehnen-type dark-matter halo. This geometry provides a remarkably simple analytic model of supermassive black holes embedded in galactic environments, having a lapse function $ f(r)=1-2 M r^{2}/(r+a)^{3}, $ [R. A. Konoplya, A. Zhidenko, 2511.03066]. The regularizing parameter $a$ is the characteristic scale of the halo. We compute the quasinormal spectrum for both axial "up" and "down" perturbations using the WKB method and verify the results through time-domain integration. The two sectors are no longer isospectral, and the deviations grow with the halo scale parameter. The grey-body factors and absorption cross-sections are extracted via standard scattering boundary conditions and the WKB approach, and their behaviour is fully consistent with the structure of the effective potentials. Altogether, our analysis demonstrates that a dark-matter halo imprint induces modifications in the gravitational response, while the employed approximation schemes remain sufficiently accurate for quantitative predictions. At asymptotically late times, the presence of the halo does not alter the Price-law decay, which remains identical to that of a Schwarzschild black hole in vacuum.