Hawking Radiation of Non-asymptotically Flat Black Holes

ABSTRACT: In this thesis, we study the Hawking radiation (HR) of non-asymptotically flat (NAF) four-dimensional (4𝐷) static and spherically symmetric (SSS) black holes (BHs) via the Hamilton-Jacobi (HJ) and the Parikh-Wilczek tunneling (PWT) methods. Specifically for this purpose, linear dilaton BH (LDBH) and Grumiller BH (GBH) or alias Grumiller-Mazharimousavi-Halilsoy BH (GMHBH) are taken into consideration. We should state that the GMHBH has the same metric structure with the GBH. The most important difference between them is the theories in which they are derived. While the GBH belongs to the Einstein’s theory, the GMHBH is the solution to the 𝑓(ℜ) theory. For the GBH, we also study the quantization of its entropy/area via the quasinormal modes (QNMs). We firstly apply the HJ method to the geometry of the LDBH. While doing this, in addition to its naive coordinates, we use four different regular (well behaved across the event horizon) coordinate systems which are isotropic, Painlevé-Gullstrand (PG), ingoing Eddington-Finkelstein (IEF) and Kruskal-Szekeres (KS) coordinates. Except the isotropic coordinates (ICs), direct computation of the HJ method leads us to obtain the standard Hawking temperature (𝑇𝐻) in all other coordinate systems. With the aid of the Fermat metric, the ICs allow us to read the index of refraction of the medium around the LDBH. It is explicitly shown that the refractive index determines the value of the tunneling rate and its natural consequence horizon temperature. But, the ICs produce an imperfect result for the horizon temperature of the LDBH. We also explain how this discrepancy can be resolved by regularizing the integral which has a pole at the event horizon. iv Secondly, we study the HR of scalar particles from the GMHBH via the HJ method. The GMHBH is also known as Rindler modified Schwarzschild BH, which is suitable to be tested in astrophysics. By considering the GMHBH, we aim not only to explore the effect of the Rindler parameter (𝑎) on the 𝑇𝐻, but to examine if there is any disparateness between the computed horizon temperature and the standard 𝑇𝐻 as well. For this purpose, we study on the three regular coordinate systems which are PG, IEF and KS coordinates. In all coordinate systems, we compute the tunneling probabilities of incoming and outgoing scalar particles from the event horizon by using the HJ equation. Thus, we show in detail that the HJ method is concluded with the conventional 𝑇𝐻 in all these coordinate systems without giving rise to the famed factor-2 problem. Furthermore, in the PG coordinates we employ the PWT method in order to show how one can integrate the quantum gravity (QG) corrections to the semiclassical tunneling rate by taking into account of the effects of self-gravitation and back reaction. Then we reveal the effects of the QG corrections on the 𝑇𝐻. Finally, we study the QNMs of the uncharged GBH. After reducing the radial equation of the massless Klein-Gordon (KG) equation to the Zerilli equation, we compute the complex frequencies of the QNMs of the GBH. To this end, an approximation method which considers small perturbations around the BH horizon is being used. Considering the highly damped QNMs in the process proposed by Maggiore, we obtain the quantum entropy/area spectra of the GBH. Although the QNM frequencies are governed by the 𝑎 term, we prove that the spectroscopy does not depend on that term. Here, the dimensionless constant 𝜀 of the area spectrum appears as the double of the Bekenstein's result. The reason of that discrepancy is also discussed. Keywords: Hawking radiation, Hamilton-Jacobi equation, quasinormal modes, linear dilaton black hole, Grumiller black hole, Rindler acceleration, quantization, spectroscopy. …………………………………………………………………………………………………………………………