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 Analyzing Various Aspects of Black Holes in Modified Gravity(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Muhammad Arslan Nasir; SP23-RMT-019; Dr. Shamaila Rani; LHR TP 9575In this thesis, we investigate the thermodynamic properties of the Bardeen-Kiselev black hole solution with a cosmological constant, focusing on stability, phase transitions, and the compressibility factor using generalized entropy corrections. By incorporating Bar row, Renyi, Sharma-Mittal, Kaniadakis, and loop quantum gravity entropy corrections, we ´ explore their impact on black hole stability and phase transitions through specific heat ca pacity, pressure, compressibility, and Helmholtz free energy. The analysis reveals that spe cific heat capacity exhibits distinct behaviors across entropy models, including regions of stability (positive specific heat), instability (negative specific heat), and divergence points indicating phase transitions. For instance, Barrow entropy shows stability for small black holes (BHs), phase transitions for intermediate BHs, and restabilization for larger BHs. Loop quantum gravity entropy highlights significant phase transitions with unique stability patterns at higher horizon radii. Pressure-volume graphs illustrate how entropy corrections influence the black hole’s equation of state. Smaller BHs often exhibit instability at low volumes, transitioning to stable phases as volume increases. Notably, the Barrow and Sharma-Mittal entropy models show smooth transitions, whereas Kaniadakis and loop quantum gravity entropy correc tions reveal more abrupt changes. The compressibility factor analyses further underscore the non-ideal thermodynamic behavior of black holes under these entropy corrections. While Barrow entropy maintains compressibility near zero, Kaniadakis and loop quan tum gravity corrections exhibit exponential divergences, highlighting significant deviations from classical thermodynamics. Finally, Helmholtz free energy graphs demonstrate entropy-corrected phase transitions ix and stability trends. Smaller BHs exhibit consistent phase shifts across all models, with larger BHs progressively stabilizing under increasing pressure. Comparative analysis indi cates that Barrow entropy provides higher stability for larger BHs, while Sharma-Mittal and loop quantum gravity corrections lead to more dynamic transitions. This comprehensive study enriches the understanding of black hole thermodynamics by bridging classical and quantum gravity perspectives. By interpreting the cosmological constant as pressure and incorporating entropy corrections, this work offers insights into black hole stability, phase transitions, and their connections to statistical mechanics and quantum gravity frameworks. These findings contribute to the broader understanding of black hole behavior in general relativity and beyond.Item Insights of Modified Entropy on Therodynamics of Black Holes in Einstein Maxwell Scalar Theory(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Ayesha Siddiqa; FA22-RMT-050; Dr. Shamaila Rani; LHR TP 9383Insights of Modified Entropy on Therodynamics of Black Holes in Einstein Maxwell Scalar TheoryItem 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.