Matter around Schwarzschild black holes in scalar-tensor theories: Absorption and Scattering

Abstract

We investigate the absorption and scattering by a Schwarzschild black hole in scalar--tensor theories of gravity, where the coupling between matter and the scalar field induces different models for the effective mass of the scalar field. In model~I, a Bondi-type mass model described by the asymptotic mass $\hat{I}{¼}_c$, horizon mass $\hat{I}{¼}_H$, and profile slope $\hat{I}»$, it is found that the absorption cross section increases with steeper $\hat{I}»$, larger $\hat{I}{¼}_c$ (especially at higher frequencies), or smaller $\hat{I}{¼}_H$. The differential scattering cross section in this model shows the strongest dependence on the horizon mass $\hat{I}{¼}_H$. When $\hat{I}{¼}_H$ exceeds a critical value for a fixed incoming wave frequency $\ddot{I}‰$, no partial wave transmits into the black hole, flattening the differential scattering cross section as a function of angle before it increases again with further increase of $\hat{I}{¼}_H$. Model~II, which considers a truncated accretion region outside some radius $r_0$, contains a potential well in its effective scattering potential. Its absorption cross section decreases in the low-frequency region as the accretion radius $r_0$ decreases, and more importantly, it shows resonance peaks at the quasibound wave frequencies due to resonances induced by the potential well. The differential scattering cross sections show dips around intermediate scattering angles when the parameters (mainly $\hat{I}{¼}_H$ and $\ddot{I}‰$) are such that the resonantly scattered and non-resonant waves interfere destructively around these angles. In both models, absorption exhibits a zero-absorption band as $\ddot{I}‰$ approaches $\hat{I}{¼}_c$ from above, and in both absorption and scattering, the effects of the parameters are found to diminish in the high-frequency limit.

12 pages, 7figures