Field perturbations in general relativity and infinite derivative gravity

In this thesis I investigate the emitted quasi normal modes for specific fields near various types of black holes, as well as look at a modified version of Einstein’s general relativity. Quasi-normal modes are not unique to black holes. In fact they can be created by any surface that is disturbed in some way, and is trying to return to the undisturbed state. The tapping of a wine glass is a good example of why quasi-normal modes are interesting to study. In the case of the wine glass, the glass will ring at different frequencies depending on how much wine is in the glass. As such, we can determine how much wine is in the glass by listening to the sound that comes from the glass. Black holes are similar in that if they are disturbed they “ring out” energy, which depends on how much matter they have and how quickly they are spinning. In the case of the modified theory of general relativity we are interested in removing what we call a 1/r potential energy divergence, where r represents the radial distance from the centres of an object. As probe gets very close to the centre of the object the potential will become very large, and tend to infinity. Infinities in theories tend to mean that there is some limit in the theory. Our goal in the modified theory of gravity is to remove this limitation that is observed in the theory of general relativity.