Absorption and scattering of massless scalar waves by Frolov black holes

TL;DR

The paper investigates massless scalar absorption and scattering by Frolov regular black holes, linking geodesic photon-sphere properties to wave behavior. It combines classical null-geodesic analysis, analytic low-/high-frequency limits, and full-wave partial-wave computations to map cross sections across frequencies and parameter space, comparing with RN and Hayward geometries. Key findings include the horizon-area convergence at low frequency, a high-frequency sinc/geodesic-dominated pattern, and near-identical spectra for spacetimes matched by critical or glory impact parameters, highlighting photon-sphere geometry as the dominant driver while regular-core details provide secondary corrections. The work demonstrates the potential of wave-based probes to test regular black hole geometries and outlines extensions to higher spins, rotation, and wave-lensing contexts.

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.

Figures (10)

• Figure 1: Null geodesics for massless particles in the background of Frolov BHs with different values of $Q$ and $\alpha$ for a fixed $b=3 r_h$. The trajectories can be derived numerically by orbit equation Eq. \ref{['eq:1order']}. We have set the initial condition $r_{\rm inf}$ at $100 r_h$.
• Figure 2: The effective potential of a Frolov BH with the parameters $Q/r_h=0.3$ and $\alpha/r_h = 0.3$.
• Figure 3: Effective potential $V_{\text{eff}}(r)$ for the $l=0$ mode of Frolov BHs.
• Figure 4: Parameter space of Frolov BHs in the $(\ell^{2},q^{2})$ plane. The blue region corresponds to configurations with an event horizon, and the solid black curve marks the extremal limit.
• Figure 5: Normalized mass $m$ of Frolov BHs for a fixed horizon radius $r_{h}=1$, restricted to the region admitting an event horizon.