Department of Mathematics
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Item Geometric Thermodynamics of Well-Known Black Holes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Syeda Rabab Fatima; CIIT/FA19-RMT-111/LHR; Dr. Abdul Jawad; LHR TP 7532We study the phase transition and thermodynamic geometries of a charged AdS black hole with a global monopole. For this purpose, we develop the thermodynamic quantities such as Hawking temperature, spe- cific heat and pressure on horizon radius in the presence of Barrow entropy. The stability of this black hole is being observed through specific heat. Also, we investigate the thermodynamic curvatures behavior of black hole by applying Weinhold and Ruppiner formulations. It is found that ther- modynamic curvatures exhibit the attractive and repulsive nature of black hole for specific constants. We also study the thermodynamic curvature of charged BTZ black hole by fixing phase space of entropy, pressure and volume on curvature, i.e., entropy-pressure corrected curvature (RSP ) and entropy-volume corrected curvature (RSV ). It is found that there present a repulsive force by the charged BTZ black hole for its molecules, qual- itatively or phenomenologically. However, RSV shows negative behavior initially which exhibits the attractive nature of charged BTZ black hole.Item Thermodynamic Quantities and Quasinormal Modes of Specific Black Holes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Yasir; FA18-RMT-049; LHR TP 6027; Dr. Abdul JawadIt is not for the sun to exceed the moon, nor does the night leave behind the day. They all float/travel, each in an orbit. (Quran 36:40) The Joule-Thomson effect and quasinormal modes (QNMs) onto regular non-minimal magnetic black hole (BH) with a cosmological constant are being investigated. For this purpose, we extract some thermodynamical parameters such as pressure P and mass M in the presence of magnetic Qm as well as electric q charge. These parameters lead to inversion tem perature Ti, pressure Pi and corresponding isenthalpic curves. Introducing the tortoise coordinate, however, the Klein-Gordon wave equation leads to the second-order ordinary Schr¨odinger equation. For this BH, computing complex frequencies of QNMs under the scalar field perturbation satisfied their boundary conditions by using the Wentzel-Kramers-Brillouin (WKB) technique. Moreover, we consider the Lorentz symmetry violating Ba˜nados, Teitelboim and Zanelli (BTZ) BH and Hairy BH of dimensionally contin ued gravity. These solutions are obtained in massive gravity and power Yang-Mills magnetic field. We utilize the general form of first law of BH thermodynamics and compute different thermodynamical quantities. The cosmological constant Λ (either positive or negative) plays an important role in BH thermodynamics when treated as a positive thermodynamical pressure. We derive corresponding equations of state and discuss the phase transitions which is comparable with chemical Van der Waals fluid. We also find out the critical points and observe that system exhibits first order small as well as large BHs phase transitionItem Dynamical Properties of Specific Black Holes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Muhammad Umair Shahzad; FA13-PMATH-005; LHR TP 5606; Dr. Abdul JawadThe present thesis comprises the study of three dynamical phenomenon such as thermal fluctuations, accretion and tidal forces of black holes/regular black holes. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations. We examine the effects of thermal fluctuations on a regular black hole of the non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal regular black hole. Furthermore, we discuss the thermal fluctuation problem by utilizing the higher order corrected entropy. We examine the thermodynamical behavior of two well-known black holes such as Reissner-Nordström Anti de Sitter black hole with global monopole and f(R) black hole in the presence of higher order corrected entropy. We also discuss the accretion problem in two phases. In first phase, we analyze the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, non-linear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. In second phase, we develop the Hamiltonian dynamical system to tackle the accretion problem. We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sftesos black hole and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. Finally, we investigate the tidal forces occurring in a Kiselev black hole surrounded by radiation and dust fluids. We also solve the geodesic deviation equation for radially free-falling bodies toward Kiselev black hole. We explain the geodesic deviation vector graphically and point out the location of the event and Cauchy horizons for specific values of the radiation and dust parameters.