Field perturbations in general relativity and infinite derivative gravity

Abstract

In the first part of this thesis we will determine the Quasi Normal Modes (QNMs) associated to spin-3/2 fields near higher dimensional Reissner-Nodström black holes, and Schwarzschild black holes which are in higher dimensional (Anti-) de Sitter space times. In order to do this we will present the idea of QNMs, and then show how effective potentials can be obtained for the spin-3/2 fields near the black holes. Where the effective potentials will give us an indication of the fields behaviour near the black hole. We then show that using the effective potential we obtain the numerical values of the QNMs by using numerical approximations. This approach will be used for each of the space times that we are interested in. We then determine what the effects of the electrical charge and asymptotic curvature are on the emitted QNMs. In the case of the electrically charge black hole we also investigate the absorption probabilities of the QNMs. In the second part of this thesis we investigate how the theory of Infinite Derivative Gravity (IDG) can be used to obtain linear metrics, which are singularity free. In this case we provide a motivation for why we need a modified theory of gravity, such as IDG, and then show how to obtain the action and propagator for this theory. From the action of the IDG we are able to produce a metric for an electrically charged massive point source. After which we obtain the metric for a rotating object with mass. We check that these metrics are indeed non-singular, by checking that the potentials in the metric remain finite in the entire region of the space time. We also ensure that the curvature scalars and tensors are non-singular in the entire region.