Department of Mathematics
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Item Warm Inflationary Dynamics of Chaplygin Gas Models with Constant Sound Speed(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) FA17-RMT-050; Azmat Rustam; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5671This study investigates the warm inflationary dynamics of Chaplygin gas models under the assumption of a constant sound speed. Warm inflation, characterized by the simultaneous production of radiation during the inflationary phase, provides an alternative to the standard cold inflation scenario by eliminating the need for a separate reheating period. In this work, the Chaplygin gas—known for its unified description of dark energy and dark matter—is incorporated into the inflationary framework to explore its viability in describing the early universe. Assuming a constant sound speed simplifies the dynamical equations and allows for analytical treatment of the system. The evolution of key inflationary parameters, including the Hubble parameter, scalar field dynamics, and radiation energy density, is examined in detail. Slow-roll conditions are derived and analyzed within the context of dissipative effects inherent in warm inflation. Additionally, cosmological perturbations are studied to evaluate the scalar spectral index and tensor-to-scalar ratio, providing a means to compare theoretical predictions with observational data. The results demonstrate that Chaplygin gas models with constant sound speed can successfully support a sustained period of warm inflation while remaining consistent with current cosmological observations. This framework offers a promising avenue for connecting early universe inflation with late-time cosmic acceleration, contributing to a more unified cosmological model.Item Dynamical Properties of Specific Black Holes(Library Information Services, COMSATS University, Lahore Campus, 2015) Muhammad Umair Shahzad,; FA13-PMATH-005; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5606Dynamical Properties of Specific Black Holes The 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 Thermodynamics of Dyadosphere of Reissner Nordstrom, f(R) Global Monopole and Janis Newman-Winicour Black Holes(Library Information Services, COMSATS University, Lahore Campus, 2016) Ayesha Sadiq,; FA14-BSM-013; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5258In this thesis, we study the effects of thermal fluctuations on Dyadosphere of Reissner-Nordstr¨om, Janis-Newman-Winicour and the fragmentation of f(R) global monopole black holes. In the presence of these fluctuations, we obtain various thermodynamic quantities like entropy, pressure, specific heat, Gibb’s free energy and Helmholtz free energy. We discuss the stability of these black holes using the γ (the ratio of heat capacities). We also discuss the phase transition, grand canonical ensemble and canonical ensemble. It is demonstrated that in Dyadoshpere of Reissner-Nordstr¨om, Janis-Newman Winicour and fragmentation of f(R) global monopole black holes become locally and globally stable with respect to increasing value of horizon radius.Item Thermal Fluctuations Of A Regular And Einstein(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Hafiza Zarish Arshad; , FA14-BSM-001; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5252In this thesis, we study the effects of thermal fluctuations on regular black hole solutions with cosmological constant and Einstein-aether black hole with coupling constant respectively. We consider the logarithmic corrected entropy in order to analyzing the thermal fluctuations on regular black hole solutions and Einstein-aether black hole. We also obtain various thermo dynamical quantities such as entropy, pressure, specific heats, Gibb’s free energy and Helmholtz free energy. We also investigate the stability of reg ular black hole solution and Einstein-aether black hole in terms of γ, phase transition, grand canonical ensemble and canonical ensemble. We analyze that regular black hole are stable when we increase the value of cosmologi cal constant and Einstein-aether black hole are stable when we increase the value of coupling constant respectively.