Aksusti̇k kara deli̇kler

In this thesis, we study acoustic black holes that mimic the kinematics of a black hole and investigate several phenomena such as the Hawking radiation and the superradiance. The particular model we employ is known as the Draining Bathtub (DBT) model in the literature, de ned in (3+1)-dimensions with a sink at the origin, where the e ective geometry possesses two horizons, inner one corresponding to the event horizon and the outer one is the ergosphere. This feature of the model o ers an opportunity to study rotating Kerr black holes, that also posses an event horizon and an ergoregion that allows an e ect called the Penrose process. In the acoustic analogy the same e ect can be viewed as super-resonance. After showing the equivalence of the equation of the motion for the sound propagation in an inviscid, barotropic, irrotational uid with the propagation of light in curved spacetime, DBT e ective metric with an event horizon and ergosphere is given. Di erential geometric methods are used to derive the Klein-Gordon PDE from the line equation of the model. The super-resonance e ect is studied by calculating the transmission and re ection coe cients of a scattered wave through the solution of the PDE at asymptotic regions. Here the super-resonance equation is also obtained through the Frobenius method applied at the singular point, on the event horizon for the model.