Scattering of scalar waves by scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity

Abstract

We systematically investigate the scattering and absorption of a massive scalar field by scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity with quartic coupling $f(ϕ)=α(ϕ^{2}+βϕ^{4})$ and exponential coupling $f(ϕ)=α(1-\operatorname{e}^{-βϕ^{2}})$. The background solutions are obtained numerically via a Chebyshev pseudospectral method, enabling a partial-wave analysis on purely numerical black hole backgrounds. The partial-wave results are cross-validated against geodesic and glory approximations and the Schwarzschild limit with excellent agreements. We find that scalarization suppresses the total absorption cross section relative to the Schwarzschild case, and produces distinctive signatures in the differential scattering cross section. A qualitative difference between the two coupling models is identified: for the quartic coupling model, deviations from Schwarzschild are concentrated in the intermediate-angle region $\sim(70^{\circ},140^{\circ})$, with comparatively small changes at forward angles and near the glory peak; for the exponential coupling model, deviations appear across the full angular range and substantially modify the glory peak, which in some parameter regimes can even exceed the Schwarzschild value. This distinctive angular pattern provides a potential diagnostic for distinguishing EsGB coupling functions from scattering observables.