Conformal invariance can ameliorate or eliminate the singularities residing in the black holes, and may still exist in the strong gravity regimes close to these black holes. In this paper, we try to probe this conformal invariance by looking into the wave absorption and scattering by the nonsingular static spherical black holes. The partial and total absorption cross section, as well as the differential scattering cross section, are presented for black holes with different choices of conformal parameters. Although the photon trajectories are unchanged from the Schwarzschild case since the spacetimes are conformally related, the wave optics are affected by the conformal parameters. As a result, the absorption of waves generally increases with the conformal parameters, while the shadow of the black holes remains the same as the Schwarzschild case. Moreover, the peaks in the oscillatory pattern of scattering shift towards smaller observing angles as the conformal parameters grows, while the widths of the glory peaks do not show sensitive dependence. The unique signature of the wave absorption and scattering by the nonsingular static spherical black holes in conformal gravity thus can serve to distinguish themselves from the Schwarzschild in the low frequency regime, and from other spherical black holes of alternative gravities in the high frequency limit and glory peaks.
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