Quantization of Euclidean Black Holes via the Adiabatic Invariance Method

In this thesis, we calculate the entropy of four different types of black holes and show that entropy and area of the considered black holes are equally likely quantized. The quantization of entropy/area of the black holes are employed by using the adiabatic invariance formulation of the famous Bohr-Sommerfeld theory. Moreover, we consider the exactness conditions of the first order differential equations to derive the integral solution of the adiabatic invariance. The black holes that are going to be discussed are the Schwarzschild black hole, the Kerr black hole, the Reissner-Nordström black hole and the Kerr-Newman black hole. In particular, the detailed derivations of the adiabatic invariance`s integral solutions for the latter three black holes, are given. At the end of each chapter, the quantization of the entropy/area spectrum for the considered black hole is proven via the Bekenstein’s area conjecture. Keywords: Black hole, Black hole area, Black hole entropy, Adiabatic invariance, Exact differential equations, Quantization of black hole entropy and area.