Scalar wave scattering from Schwarzschild black holes in modified gravity

We consider the scattering of gravitational waves off a Schwarzschild black hole in $f(R)$ gravity. We show that the reflection and transmission coefficients for tensor waves are the same as in General Relativity. While the scalar waves, which are not present in General Relativity, demonstrate interesting features. The equation that governs these scalar waves can be reduced to a Volterra integral equation. Analysis of this equation shows that a larger fraction of these waves are reflected compared to what one obtains for tensors. This may provide a novel observational signature for fourth order gravity.