M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Isotropization and New Solutions for Self-Gravitating Systems with Zero Complexity(2025) Maida Aslam; CIIT/SP24-RMT-021/LHR; LHR TP 10081This thesis explores the compact stellar structure in the context of the F(R,LM,T) gravity theory, employing the Minimal Geometric Deformation (MGD) technique via gravitational decoupling (GD). Starting with the isotropic Durgapal-Fuloria (DF) solution, we construct its anisotropic extension and develop two additional models by imposing vanishing and equal complexity factor conditions. The complexity factor, derived from the Riemann ten- sor’s orthogonal decomposition, serves as a key tool to understand the structural intricacies of self-gravitating systems. The physical viability of the models is tested against observa- tional data from the pulsar PSRJ0740 + 6620, using mass and radius constraints obtained from NICER and XMM-Newton observations. A detailed graphical analysis is conducted to study the radial behavior of energy density, pressure components, and anisotropy, and the parameter space ensuring physical viability is summarized in tabular form for each model.Item Exploring the Existence of Non-Commutative Wormholes in Scalar Tensor Theories(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) TAHREEM GHAFFAR; CIIT/SP20-RMT-008/LHR; Dr. Muhammad Zubair; LHR TP 7645Scalar tensor theories appear as handy candidate to analyze the stellar objects like compact stars and wormholes. In this thesis, we have discussed about the non commutative spherically symmetric wormhole solutions in f(R, Φ) gravity. For this purpose, we consider two different frameworks such as Gaussian distri- bution as well as Lorentzian distribution non commutative geometry. With the help of Gaussian and Lorentzian distribution we have found the exact and nu- merical solutions of the non commutative wormhole’s in f(R, Φ) gravity. By con- sidering suitable values of the unknown parameters, we analyse the different characteristics of the wormhole’s models analytically as well as graphically.It has been observed that without involving any exotic material it is feasible to acquire wormhole’s solution in this theory.For this purpose firstly we consid- ered the different categories of fluids i.e an isotropic, anisotropic and barotropic fluids. For all these fluids we analyzed the energy conditions to examine the f(R, Φ) gravity. To check the energy conditions we have calculated b(r) numer- ically as well as graphically in order to check whether the wormhole solutions exist or not. It has been concluded that the solution we obtained is idealistic. We have also analyzed the energy conditions (NEC and WEC) in detail. We have concluded that for the existence of non commutative wormhole’s solution these energy conditions are valid. And also for these cases, we observed that for anisotropic fluid, realistic wormhole geometries can be constructed that satisfy the energy conditions. We find the shape function which protects the worm- hole throat and enables us to discuss the requirement of exotic matter. We also analyze the energy constraints using the graphical schemes.Item Extension of Isotropic Solutions into Anisotropic Domain Via Gravitational Decoupling Approach(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MOBEEN AMIN; CIIT/FA19-RMT-048/LHR; Dr. Muhammad Zubair; LHR TP 7437In this thesis, we study known charged and uncharged isotropic Heintzmann solution and Durgapal IV solution and extend it to its well anisotropic domain by manipulating gravitational decoupling through extended geometric defor- mation (EGD) approach. We employ linear transformation on both metric po- tentials and convert the single set of EFEs into two less-complicated subsys- tems. The first one is related to the standard Einstein-Maxwell field equations (EFEs), while the other one is related to additional source. The matching con- ditions at the stellar surface are discussed in detail, where outer geometry is represented by Reissner-Nordstrom solution in the presence and schwarzschild solution in the absence of charge and also evaluate the expressions for ther- modynamical quantities ρtot, ptot r and ptot t using mimic constraint and equation of state (EoS).We discuss the physical properties of the stellar model. Physical analysis is carried out using different physical indicators i.e, energy conditions, equilibrium equation, casualty condition, Herrera’s cracking concept, adiabatic index, compactness and surface redshift. In order to check the viability of the anisotropic version of the solution, we consider three different realistic stars, namely SAXJ1808.4 − 3652, SMCX − 4 and PSRJ1614 − 2230, and analyze the behavior of the model against different values of intensity parameter, i.e., γ = 0, 0.2 and 0.3 and also evaluate the graphical behavior of compact star PSRJ1614 − 2230 against different values of γ = 0.25, 0.55 and 0.75 for different model.Item Cosmological Bouncing Solutions With Different(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Muhammad Ehsan Khalid,; FA17-RMT-020; Dr. Muhammad Zubair,; LHR TP 5653Cosmological bouncing scenarios provide an alternative to the standard Big Bang paradigm by replacing the initial singularity with a finite minimum scale factor, followed by a transition from contraction to expansion. In this work, we investigate a class of bouncing solutions arising from different theoretical frameworks, including modified gravity theories, scalar field dynamics, and quantum cosmological effects. By analyzing the behavior of the Hubble parameter and the evolution of the scale factor, we identify the necessary conditions for a successful, non-singular bounce. Particular attention is given to the role of energy conditions, stability criteria, and the avoidance of ghost and gradient instabilities. We compare the physical viability of various models and discuss their implications for early-universe evolution, structure formation, and observational signatures in the cosmic microwave background. Our results demonstrate that a wide range of theoretical approaches can consistently produce stable and realistic bouncing cosmologies, offering promising alternatives to inflationary scenarios.Item Some Cosmological Implications Of Extended Scalar(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Farzana Kousar; SP13-PmAth-006; Dr. Muhammad Zubair; LHR TP 5607This thesis is devoted to explore some cosmological implications in gravity and generalized reconstruction of gravity. Initially, we discuss the cosmological theory (where , and represent the Ricci scalar, scalar invariant and scalar field) corresponding to power law and de Sitter evolution in the framework of FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some known forms of these conditions in general relativity, and theories. We also present the general constraints in terms of recent values of snap, jerk, deceleration and Hubble parameters. The energy bounds are analyzed for reconstructed as well as known models in this theory. Finally, the free parameters are analyzed comprehensively. First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in gravity. In this modified theory, Friedmann equations are formulated for any spatial curvature. These equations can be presented into the form of first law of thermodynamics for ̂ ̂ , where ̂ is an extra entropy term because of the non-equilibrium presentation of the equations and ̂ for the equilibrium presentation. The generalized second law of thermodynamics (GSLT) is expressed in an inclusive form where these results can be represented in GR, and gravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters. Moreover, we examine static spherically symmetric wormhole solutions in generalized gravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore different models and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. From our results, one can conclude that for all three cases of fluids stable and realistic wormhole solutions can be constructed. Further, we have considered action which is non-minimally coupled to the x scalar field. In this context, we obtain the exact analytical solutions for inflationary era as well as find a graceful exit condition from inflation. We calculate the perturbed parameters, i.e., number of e-folds, slow-roll parameters, scalar and tensor power spectra, corresponding spectral indices and ultimately tensor to scalar ratio. It is showed that the power spectra lead to blue-tilt for this model. The trajectories of the perturbed parameters are plotted to compare the results with recent observations. Finally, we will discuss cosmological models using Bianchi type I for anisotropic fluid in theory of gravity which involves scalar potential. For this purpose, we consider power law assumptions of coupling function and scalar field along with the proportionality condition of expansion and shear scalars. We choose two models and obtain exact solutions of field equations in both cases. For these constructed models, the behavior of different physical quantities like EoS parameter, self-interacting potential as well as deceleration and skewness parameters is explored and illustrated graphically for the feasible ranges of free parameters. It is concluded that anisotropic fluid approaches to isotropy in later cosmic times for both models which is compatible with the observational data.Item Anisotropic Stellar Models in Matter Coupled Teleparallel Modified f(T; T ) Gravity(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Muhammad Junaid Kamran; FA19-RMT-065; LHR TP 7408Since the last decade, the expansion of the universe has been a major issue of debate. It was recently debated under topics like as the radiation era (early-time expansion), also known as the inflationary (rapid expansion) era, and the latetime cosmic expansion (dark energy) period. In this thesis, we concentrate on the study of anisotropic stars with anisotropic matter distribution in the framework of f(T; T ) = _T(r)2 + _T (r) model, here _, _ are represent the arbitrary constants, T and T represent, trace of stress energy-momentum tensor and torsion scalar, respectively. This model has interesting cosmological properties, in addition to providing an effective dark energy sector explanation [13]. In order to attain our target, we considered the Krori-Barua space-time and utilize the off-diagonal tetrad components for deriving the corresponding set of field equations. We evaluate the effective density (_eff ), effective radial (peff r ) and tangential pressure (peff t ) using the EoS of strange star i.e., MIT bag model pr(r) = 1 3 [_(r) 4Bg]. In chapter IV we explored anisotropic strange stars by applying karmarker condition without MIT bag model in the background of "f(T; T )" gravity and for the unknown constants aries in the solution have been evaluated by using the conventional matching of interior and exterior space time. Now for checking the feasibility of our model we discuss the anisotropy, energy condition, TOV forces, abreu condition, EoS parameters, adiabatic index, mass function, compactness and redshift for different compact stars models namely, PSRJ1416 2230, 4U1608 52, CenX 3, EXO1785 248 and x SMCX 1.Item An Anisotropic Version of Tolman VII Solution in Rastall Theory of Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Dawood Falik Sher; FA18-RMT-022; LHR TP 6457; Dr. Muhammad ZubairIn our research, we worked for self gravitating system to evaluate stellar in- terior’s possibilities. For this we describe an anisotropic matter distribution , which is based on the Rastall’s theory of gravity with the help of minimal geo- metric deformation approach. As the minimal coupling matter principle is bro- ken down by the Rastall’s gravity, hence we have to provide an exhaustive ex- planation. This explanation deals with Israel-Darmois junction conditions and how it works in this pattern. Further, we have obtained the deformed space- time and use the procedure of mimic constraints. For checking the viability of any proposal, the results has been applied to any well known solution. So as we do. We use famous Tolman VII solution, to check the viability. The whole description of thermodynamical effects presented by the additional sources in mentioned. In addition, we have compared the results with their similes in the shadow of pure general relativity, pure Rastall’s gravity and, also in the struc- ture of general relativity which includes "gravitational decoupling". For mathe- matical and graphical analysis we take α i.e., gravitational decoupling constant and λ i.e., parameter of Rastall as free parameter. The compactness factor which describes the general relativity is taken as 0.2. Besides, in order to get more realistic picture, it requires to bound the parameters α and λ both through the use of real observational data to get the limits of the theory under this model. This methodology suggested to study the applications of neutron and quark stars. Our work also deals with the extended minimal geometric deformation. ixIn this section we check how temporal component effects the value of total en- ergy density, total redial and tangential pressure, anisotropy of pressure, energy conditions and stability conditions. For this we again use famous Tolman VII solution for the values of ν and µ and check the results. The metric potential of this solution is in the form of exponent, hence we use the rules function (ln) to get the suitable values of components. This section show very interesting results as we will discuss in chapter 3 in detail.Item Dynamical Analysis of Self-gravitating Cylindrical Objects in f (R, T ) Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Hina Azmat; FA15-RMT-010; Dr. Muhammad Zubair; LHR TP 6823The exploration of stability or instability range in modified theories provide deep insight of gravitational interaction in current era which is based on the ex pansion of the universe. In this thesis, we have analyzed cylindrically symmet ric self-gravitating objects for stability analysis within the framework of f(R,T) gravity. This alternative theory provides substitute to dark energy (DE) which assumes high negative pressure and is considered to be responsible for cosmic expansion. In this discussion, we have considered cylindrically symmetric systems with anisotropic matter distribution. The modified field equations and dynamical equations are constructed in f(R,T) theory of gravity. First order perturbation is applied on the modified field equations and dynamical equations which facil itates the construction of the collapse equation. Instability ranges are explored in both Newtonian(N)andpost-Newtonian(pN)eraswiththehelpofadiabetic index Γ which measures the pressure variation with changing energy density. Some conditions are imposed on material variables that are required for stable configuration. Cylindrically symmetric sources evolving under expansion-free condition are analyzed with locally anisotropic distribution . The collapse equation of cylin drical star is obtained by adopting perturbation approach for general solutions of gravitational field equations and conservation equations. Dynamical insta bility is discussed in N and pN regimes, stability constraints have also been ix developed. The adiabatic index ‘Γ’ is found to be meaningless for the discus sion of stability of gravitating sources carrying expansion-free condition, while stability variations are determined by physical properties of the fluid. Stability analysis for shearing viscous anisotropic fluid with cylindrical symmetry has also been made in f(R,T) theoryItem Stellar Structures in modified gravity based on Karmarkar Condition(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Allah Ditta; FA18-RMT-045; LHR TP 6025; Dr. Muhammad ZubairUniverse expansion has been a hot topic of discussion since the last decade. Not long ago, it remained in discussion under ways of interest like, radiation era ( early-time expansion) also known inflationary (rapid expansion) era, late time cosmic expansion (dark energy) era etc. Thesis understudy discusses the acceleration phenomenon of the Universe in cosmology by narrating different configurations of compactobjects bytakingintoaccountthefluidofanisotropic. Here we use f(T) gravity, which is originally a real and approximate modifica tion of TEGR. We carry our study with a well-known models f(T) = βTn and f(T) = T − α (T 6 )m1 + β(T 6 )m2 of f(T) gravity where T is torsion scalar, α, β are real constant, and n,m1,m2 are integers greater or equal to 2. For the con struction of stellar structures, we use spherically symmetric space-time as it is considerably near to nature. Embedding class one approach which is famous as Karmarkar condition is a useful technique to evaluate the metric components. This techniquelinks bothofthepotentialcomponentsofthemetricfunctioninto a unified differential equation. We assume the grr component of the space-time with the required potential. Using the Karmarker condition, one can fond the gtt component of metric function by solving the differential equation which links the gravitational metric potentials. We calculate the values of constants used in modeling by comparison of interior and exterior space-times through junc tion condition. For this motive, we utilize the observed data of compact star PSRJ1614-2230 for values of radius and mass. We ensure the stability and vi ability of our model through a detailed and comprehensive inspection of TOV ix equation, EOS, speeds of sound, casualty conditions, Redshift, compactness, and mass function graphically.