Scalar perturbations of Schwarzschild black holes in modified gravity.
This thesis is concerned with the physics related to scalar perturbations in the Schwarzschild geometry that arise in modifed gravity theories. It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures on the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this thesis we consider the perturbations of the Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equations that govern these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. We also show that higher order curvature corrections to General Relativity, in the strong gravity regime on scales of the order of the near horizon, produce a rapidly oscillating and infalling Ricci scalar fireball just outside the horizon. These fluctuations behave like an infalling extra massive scalar field that can generate the ringdown modes of gravitational waves having the same natural frequency as those that are generated by black hole mergers. Our analysis provides a viable classical or semi-classical explanation for the echoes in the ringdown modes without invoking the existence of any exotic structures at the horizon.