Scattering of Scalar Wave by Extended Black Hole in f ( R ) Gravity

Abstract

We analyze the Schrödinger-type scalar wave equation of an extended black hole in 𝑓 (𝑅) gravity, and numerically investigate its absorption/scattering cross sections using the partial wave method. It is found that the dimension of length 𝛼 makes the peak value of the effective scattering potential fall down, and the absorption cross section oscillates around the geometric optical value in the high frequency regime. We can also see that the scattering flux becomes stronger and its angle width becomes narrower in the forward direction, the glory peak becomes lower and the glory width becomes narrower along the backward direction when the coupling parameter 𝛼 increases.