Greybody factor for rotating linear dilaton black holes

After the general relativity was come to light, black holes have been thought both as the answer and the comprising of the many questions about physics of the universe. It was immediately followed by spherical symmetric static solution of Einstein Field Equations known as Schwarzschild solution which describes the space-time out of a star. Schwarzschild solution was examined in detail later and it was found that the solution has two kinds of singularities; one is coordinate singularity that can be removed by a coordinate transformation and an essential curvature singularity which can not be removed by coordinate transformation at the center. These objects are called black hole,then. Say the least of it, black holes are the physical objects that contains huge amount of mass in the very tiny area. Therefore, the gravitational field of black holes are so strong and even the light cannot be able to revolt this force. Charged and rotating black hole solutions are found and presented in the literature, later. Classically, black holes are stable objects and they do not radiate. After the study of Hawking about quantum field theory in a black hole background, he revealed that black holes are thermal systems and they may emit particles so-called Hawking radiation, until they run off their energy. Since, in the frame of this theory, a black hole is not actually black and according to its emission process it may not live forever. Hawking radiation behaves like a black body at the event horizon of the black hole. However, due to the space-time geometry of the black hole background, the initial radiation is distorted passing through the potential of the black hole and goes to observer at infinity. Therefore, the observer at the infinity, cannot measure the black body spectrum of the black hole, instead one measures filtered Hawking radiation in a sense. This quantity that determines how the black body radiation altered is called greybody factor. Greybody factor is basically the transmission probabilities of the Hawking radiation through the corresponding space-time. Scattering process takes place for movement of the radiation. Due to calculate the transmission coefficients and greybody factor, different types of approaches are examined such as simple matching technique, monodromy technique. Since greybody factor is a frequency dependent quantity, or these techniques are applied for different frequency regimes. In the first chapter of this study, after the black holes and Hawking radiation are briefly explained, greybody factor are defined according to this concept. Then the previous works related with calculation the greybody factor of black hole background are reviewed. With this revision, it is realized that there are several approaches to derive the greybody factor depend on the frequency regime. In this thesis, since the greybody factor is examined for low frequency regime for Schwarzschild- like and rotating linear dilaton black hole backgrounds, semiclassical matching technique is investigated through the study. In the second part, after giving a brief introduction to thermodynamic behavior of black holes, Klein-Gordon equation for massless scalar field is constructed for four and five dimensional uncharged, static Schwarzschild-like black hole and Schrödinger-like form of the equations are found with respective effective potentials. Therefore, Klein-Gordon equation with massless scalar field for d- dimensional Schwarzschild- like black hole is generalized and transformed to the Schrödinger-like equation to express the black hole background as a potential barrier for the radiation and giving a deviation from the black body radiation spectrum as seen by an asymptotic observer. Then scattering theory of this type of black holes are reviewed to infer that greybody factor can be calculated not only by examine the scattering of a conjectural outgoing wave from horizon but the scattering of an incoming wave from infinity. This inference is the crucial part of the calculation of greybody factor. Also this choice reveal that the black hole are taken as classical black holes not semiclassical. The third chapter comprises the properties of the rotating linear dilaton black hole background for non asymptotically flat spacetime and the derivation of the greybody factor for this background according to Sakallı' s study. The matching of the solution of near horizon region with asymptotic region gives the relation between the flux of these regions. For the last chapter, phenomenon of superradiance is studied. Firstly, superradiance amplification of massive scalar fields in the Kerr black hole is reviewed according to Betri's study and superradiance condition for this black hole is found as $\omega