Scalar wave scattering from Schwarzschild black holes in modified gravity

TL;DR

This paper investigates how gravitational waves scatter off Schwarzschild black holes in modified gravity, revealing that scalar waves exhibit increased reflection, potentially serving as observational signatures of such theories.

Contribution

It demonstrates that scalar waves in $f(R)$ gravity show distinct scattering behavior compared to tensor waves, offering a new way to test modified gravity theories.

Findings

Scalar waves are more reflected than tensor waves.

Reflection coefficients for tensor waves match General Relativity.

Scalar waves could serve as observational signatures of $f(R)$ gravity.

Abstract

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.