Bosonic and Fermionic Greybody Factors of Fourdimensional Black Holes in Various Theories

This PhD thesis examines the bosonic and fermionic greybody factors of fourdimensional black holes (BHs) in various theories. A high-energy collision creates a BH that evaporates through Hawking radiation (HR). One of the most important quantum quantities of a BH is the BH gravitational factor (GF), is the HR fraction that can reach the known spatial infinity. GFs have the potential to carry a significant amount of information that could drive the theory of quantum gravity. When HR is scattered from the gravitational potential, part of it returns to BH, while the other part is transmitted to spatial infinity. In this context, the GF is also known as the transmission probability. A very high GF value indicates a high probability of HR to reach spatial infinity. By calculating the GF radiation in various ways, we shall first derive the Schrödinger equation because it represents a kind of wave equation that applies to matter waves. For this purpose, we use the Klein-Gordon equation for scalar perturbation (bosonic particles) and the Dirac equation for fermionic perturbation (fermionic particles), which are discussed in Chapters 4 and 5, respectively. In fact, the GFs will be determined by the associated effective potential of the wave equation. In short, the detailed analysis of the GF via different methods are given in this thesis. In the framework of general relativity (GR), the radiation of gravitational waves has an important phase defined by the appropriate oscillation frequencies of BH. These frequencies are called quasinormal modes (QNMs), which depend on the BH parameters. The propagation of QNMs is different from the classical normal modes. That is, while the real parts of the characteristic complex frequencies obtained represent the frequency of oscillation, the imaginary parts represent the damping ratio. We shall employ a semi-analytical technique, the sixth order WKB approach, to calculate the QNMs of the BHs that we consider in this thesis.