Absorption and scattering of massless scalar waves by Frolov black holes

Abstract: We comprehensively investigate the absorption and scattering of massless scalar waves by Frolov black holes, which is a class of regularization of the Reissner--Nordström spacetime. By analyzing the null geodesics, we determine the photon sphere radius and the critical impact parameter, deriving the geometric capture cross section and the classical differential scattering cross section. Utilizing the partial-wave method, we numerically compute the absorption and scattering cross sections across a broad frequency range. Our numerical results show excellent agreement with the low-frequency limit and the high-frequency sinc approximation, as well as with the semiclassical glory approximation. We analyze the dependence of the spectra on the charge and the regularization parameter (Hubble length). Under the horizon-radius normalization, we observe that the total absorption cross section increases with the regularization parameter, a behavior we attribute to the variation of the dimensionless mass. Furthermore, by comparing Frolov, Reissner--Nordström, and Hayward black holes, we demonstrate that their absorption and scattering patterns are nearly indistinguishable when their critical impact parameters or glory impact parameters are matched. This indicates that the photon sphere geometry predominantly governs scalar field interactions, while the detailed core structure plays a secondary role. Our work underscores the potential of wave-based probes to test regular black hole geometries and their observable imprints.