Department of Mathematics
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Item Effects of Modified Entropy on Black Hole Thermodynamics in Bumblebee Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Zainab Nazish; CIIT/SP24-RMT-019/LHR; Dr. Abdul Jawad; LHR TP 10080This thesis explores the thermodynamic behavior and stability of anti-de Sitter (AdS) black holes within the framework of bumblebee gravity, a theory in which Lorentz symmetry is spontaneously broken by a vector field. The study examines how the Lorentz-violating bumblebee parameter influences the event horizon structure and various thermodynamic properties in both standard and extended phase spaces. Thermal stability is analyzed through heat capacity and Helmholtz free energy. The results show that large bumblebee AdS black holes can simultaneously satisfy local and global stability conditions, with the stable regions strongly depending on the Lorentz-violating parameter. The research also investigates heat capacity at constant pressure in the extended phase space, where the cosmological constant is interpreted as thermodynamic pressure. In this case, the stability criteria are found not to be fulfilled, highlighting the significant role of Lorentz symmetry violation in black hole thermodynamics. In addition, the thesis studies the sparsity parameter and Hawking radiation emission rates for black hole solutions in bumblebee gravity using generalized entropy models, including Sharma–Mittal entropy and three-parameter entropy indices. The findings reveal that changing the sign of the cosmological constant significantly affects thermodynamic sparsity and entropy behavior. A negative cosmological constant reduces sparsity while increasing entropy, indicating a denser thermodynamic system. Conversely, a positive cosmological constant preserves higher thermodynamic sparsity. Furthermore, the emission spectrum becomes sharper for negative cosmological constant values, indicating enhanced low-energy emission within a confining AdS background, while a positive cosmological constant generally suppresses the emission rate.Item Cosmic Implications of Tsallis Holographic Dark Energy with Various IR Cutoffs in Horava- Lifshitz Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Mehwish Shad; CIIT/SP20-RMT-024/LHR; Dr. Abdul Jawad; LHR TP 7653Horava-Lifshitz gravity is a very fascinating proposal of modified gravity for explaining the current acceleration and other cosmic issues. In contin- uation of this discussion, we study the consequences of Tsallis dark energy with Hubble and particle horizons in the framework of deformed Horava- Lifshitz gravity by taking into account flat FRW universe. The interaction between Tsallis holographic dark energy and dark matter are also taken into account to discuss the underlying scenario. It is found that fractional dark energy density (ΩD) approaches to 0.70+0.03 −0.03 as redshift goes to zero (present epoch) for both cases of horizons. The cosmic parameter (ωD) shows phantom crossing behavior in both models, i.e., it evolutes the uni- verse from quintessence phase to phantom phase by crossing the vacuum horizon. In both cases of horizons, the deceleration support the cosmic ac- celeration by exhibiting the negative values. The perturbation sound speed also favors the viability of our models through positive behavior. The co- incidence parameter support the exchange of dark matter to dark energy phenomenon through positivity. We also discuss the behavior of growth rate and growth index in the growth of matter density perturbations for both horizons. These parameters mimic the ΛCDM behavior of the universe.Item Cosmic Acceleration in Modified Horava- Lifshitz Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Sameen Ashraf; CIIT/FA19-RMT-094/LHR; Dr. Abdul Jawad; LHR TP 7395We discuss the cosmological implications of the interacting Barrow holo- graphic dark energy model in the context of flat deformed Hoˇrava-Lifshitz gravity by assuming the interaction (Γ) between dark energy and pressure- less dark matter. To understand the mechanism of recent accelerated ex- pansion of the universe, we consider Hubble and event horizons as infrared cutoff. We investigate the evolutionary history of cosmological parame- ters especially the equation of state, Hubble, deceleration, squared speed of sound and find results that favor observational data of Planck 2018. It is found that the Hubble parameter lies in the range 72+2 −2 (for event horizon) and 74.004+0.004 −0.004 (for Hubble horizon). The equation of state parameter pro- vides the phantom phase of the universe, while the deceleration parameter illustrates the accelerated phase of the universe. On the other hand, we plot the squared speed of sound and find the positive behavior which ensures the stability of underlying model. Moreover, we examine the generalized second law of thermodynamics of this cosmological system with barrow entropy as horizon entropy and observe that this law holds for both horizons.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 Cosmic Inflation Evading Swampland Conjectures(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Kashaf Embreen; CIIT/FA19-RMT-022/LHR; Dr. Abdul Jawad; LHR TP 7440In this thesis, we study the inflationary scenario in the realm of k-essence model and swampland conjecture. Taking into account three models of Chaplygin gas, that is, generalized, modified and generalized cosmic Chap- lygin gas models, we discuss the slow roll parameters (²(φ), η(φ)), curvature perturbation (Ps), tensor to scaler ratio (r) and scaler spectral index (ns). In reference to k-essence model, the coupling function as a function of scaler field L(φ) is used. We investigate the swampland conjecture and then find the value of ζ(φ) i.e bound of second conjecture for the above three models by unifying swampland conjecture and k-essence. We plot the inflationary parameters and bound of swampland conjecture r −ns, ζ(φ) − φ, and check their values according to Planck data 2018.Item Inflationary Dynamics and Thermodynamics of Chaplygin Gas Models(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Adeel Sultan; CIIT/SP17-RMT-006/LHR; Dr. Abdul Jawad; LHR TP 5441In this thesis, we study the reconstruction of warm inflation model with the help of tensor to scalar ratio (r) and scalar spectral index (ns) in terms of number of e-folds (N). In this regards, we take flat FRW metric and discuss the general forms of dissipative coefficient Γ(φ, T ) as well as effec- tive potential V (φ, T ) for two dissipative regimes i.e., the weak and strong. We use inflationary parameters like slow roll parameters, power spectrum of the curvature perturbation, tensor spectrum, spectral index, scalar to tensor ratio and Hubble parameter to find the generalized form of dissi- pative coefficient and effective potential. Further, we discuss generalized cosmic Chaplygin gas in the scenario of particle creation. We examine energy density (ρ), Hubble parameter (H), declaration parameter (q), tem- perature (T ) and particle number density (n) under three different models of particle creation rate. We also analyze the production of entropy and Bekenstein entropy in the scenario of first law of thermodynamics. We dis- cuss the validity of generalized second law of thermodynamics and thermal equilibrium under three models of Γ and discuss the graphical behavior of above mentioned terms.Item Dynamical Properties of Specific Black Holes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Muhammad Umair Shahzad; CIIT/FA13-PMATH-005/LHR; Dr. Abdul Jawad; LHR TP 5606The 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.Item Swampland Criteria of Inflationary Cosmology with Well-Known Potentials(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Aneesa Majeed; CIIT/FA19-RMT-115/LHR; Dr. Abdul Jawad; LHR TP 7383We explore the swampland conjectures of quintessence and tachyon scalar field models in f(T ) and Einstein gravities, respectively. In f(T ) gravity, we consider cold and warm (by assuming generalized dissipative coefficient) inflationary scenario and develop constraints on de-Sitter con- jectures through Bekenstein entropy relation. In usual inflation, the de- Sitter conjecture constraint becomes constant (in terms of models constant parameters) which can be easily analyzed for its validity (i.e., |V 0| V ≤ O(1)). However, in warm inflation, we analyze the de-Sitter conjecture constraint through T 0V TV 0 , i.e., if T 0V TV 0 < 1 then |V 0| V ≤ O(1) and hence we can obtain required result. For evaluating this condition, we choose three well-known potentials such as monomial chaotic, hilltop and generalized exponential. It is observed that the condition T 0V TV 0 < 1 satisfied for all three potentials in both regimes of dissipative coefficient for specific choice of constants. Sim- ilarly, we also obtain satisfactory results of de-Sitter conjecture for tachyon and polytropic (with quintessence scalar field) in general relativity.Item Phase Space Analysis and Cosmic Parameters of Dynamical Dark Energy Model(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Ruqia Arif; SP23-RMT-027; Dr. Abdul Jawad; LHR TP 9581This thesis explores the stability analysis of Friedmann-like spacetimes using dynamical system methods. For this purpose, we begin by considering a modified cosmological sce nario based on Tsallis entropy corrections. These entropic formulations modify the cosmo logical field equations that govern the universe’s dynamics. We incorporate these modified Friedmann equations and convert them into a first-order autonomous system of differential equations. To identify the system’s equilibrium points, we consider the interaction between cosmological fluids. Various linear and non-linear forms of interaction models are exam ined. For each model, we calculate the critical points and discuss their behavior associated with eigenvalues. We investigate the different stages in the universe’s evolution including dust and radiation dominated era of the universe as well as quintessence, ΛCDM and phan tom regimes. In addition, we develop the phase space portraits of all the interaction models revealing the stable, unstable and saddle behavior of critical points. In most of the cases, the system supports stable critical points.Item Modified Entropy Inspired Scalar Field Cosmic Inflation with Well-known Potentials(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Hafiza Iqra Nadeem; FA22-RMT-022; Dr. Abdul Jawad; LHR TP 9377This thesis is dedicated to discuss the inflationary setup with the help of modified Barrow entropy with f(R) gravity framework. We derive the Friedmann equations by using the first law of thermodynamics. With the help of these equations, we reconstruct f(R) gravity model to establish the relationships governing scalar and tensor perturbation power spectra and interestingly this model mimics thermodynamically under the slow-roll approximation. Two different types of potentials like the β potential and the exponential potential are used to explore the insights of inflationary parameters in the underlying scenario. Thus, the inflation-related quantities like scalar spectral index and tensor-to-scalar ratio are discussed graphically in our scenario by developing contour plots. It is worthwhile mention here that our results are consistent with Planck 2018 data.