Department of Mathematics
Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21
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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 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.