M.Phil / MS

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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 7437
In 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.
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 5607
This 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.

M.Phil / MS

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