Department of Mathematics
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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 4D Black Holes and Their Parameters(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Sania sobedar; SP23-RMT-036; Dr. Muhammad Zubair; LHR TP 9576Black holes are among the most enigmatic objects in the universe, characterized by their immense gravitational pull and profound influence on surrounding matter. In this thesis we considered Dyonic Modmax black hole, which is static and we apply Newman-Janis Algorithm to make the black hole rotating. The rotating metric then explored to study parametric constraints and frequencies of black hole by using the Quasi-Periodic Oscilla tions. Moreover, we investigated the effective potential. We also find the orbital frequency (or Keplerian frequency) of Dyonic ModMax black hole. It is the frequency of a particle which is orbiting around the BH. In general, it is function containing charge and radial distance of a particle from BH.Item Existence and Stability of Neutron Stars in Minimally Coupled Gravity(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Fahad Hainf; FA22-RMT-042; Dr. Muhammad Zubair; LHR TP 9378Relativistic stars’ equilibrium and stability evolved as an exciting aspect in both modified theories of gravity and GR. When these systems reflect movements and make an effort to maintain stability, they attract a lot of attention. The dynamical analysis of gravitating systems plays key role in structure formation that is why astrophysicists and cosmologists pay great attention in the discussion of stability range of gravitating sources.Here, we shall analyze the stability of NSs by analyzing the evolution of hydrostatic equilibrium configu ration for the choice of EoS p = ω(ρ4B), with ω = 1 3 and B represents Bag constant. In this scheme we pick the minimally coupled F(R,T) gravity of the form F(R,T) = R+2λT, λ stands as the coupling parameter. We will compare our results with recent observational data.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.