Hawking Radiation of Warped Anti de Sitter and Rotating Hairy Black Holes with Scalar Hair

This thesis mainly focuses on the Hawking radiation (HR) evacuating from the surface of the objects that have earned a reputation as the most extraordinary objects existing so far; the black holes (BHs). Throughout this study, quantum tunneling (QT) process serves as the model for the HR of scalar, vector and Dirac particles. The scalar and Dirac particles are anticipated to be tunneling through the horizon of rotating scalar hairy black holes (RHSBHs); whilst the vector particles are associated with a rotating warped anti de-Sitter black hole (WAdS3BH) embedded in a (2+1) dimensional fabric. It is no coincidence that for all three cases; the standard HT expression is derived. Additionally, the engagement of conformal field theory (CFT) with anti de-Sitter (AdS) space presents itself to the reader and the methodologies of Klein-Gordon equation (KGE), Dirac equation and Proca equations (PEs) are introduced. For all three cases, Hamilton-Jacobi (HJ) approach is used, together with Wentzel-Kramers-Brillouin (WKB) Approximation. Finally, the BH structures are compared with thermodynamics to derive HT with the aid of Boltzmann factor. Keywords: Hawking radiation, quantum tunneling, Klein-Gordon equation, Dirac equation, Proca equation, scalar hair, Hamilton-Jacobi method, quantum gravity.